Adding Rational Expressions

Adding Rational Expressions An expression which can be represented as a ratio of two polynomials i.e., in numerator there will be a polynomial and in denominator there will be another different polynomial because if the polynomial would be same to both numerator and denominator then the ratio becomes 1 and 1 is not a rational number. Example of rational expressions: - (2x^2 + 5) / (x + 5) (3x^2 + 2x + 4) / (x^2 + 9x + 8) (x + 2) / (x + 5) 1/ (x^2 + 5): - 1 is present to the numerator and 1 is a constant polynomial so this is also a rational expression. (x^3 + 5x^2 4x +9): - This expression can be represented as (x^3 + 5x^2 4x +9) / 1. 1 is a constant polynomial; both numerator and denominator contain polynomial so it is a rational expression. Examples of adding rational expressions: - Add the following rational expressions: - 1) (x^2 + 1)/(x +1) and 2x/(x +1) 2) 1/x , (3x^2+ 2x + 5)/2x and (2x^2 + 5x + 3)/4x Solution: - 1) (x^2 + 1) / (x +1) + 2x/ (x +1) =(x^2 + 1 + 2x) / (x + 1) = (x^2 + 2x + 1) / (x+ 1) = (x + 1)^2 / (x+ 1) = (x+ 1) 2) 1/ x + (3x^2+ 2x + 5) / 2x + (2x^2 + 5x + 3) / 4x =[4 + 2((3x^2+ 2x + 5) + (2x^2 + 5x + 3)] / 4x = (4 + 6x^2 + 4x + 10 + 2x^2 + 5x + 3) / 4x = (8x^2+9x+17)/4x

How Maths Can Help You Learn to Draw

How Maths Can Help You Learn to Draw Can Drawing Lead to Mastering Maths and Vice Versa? ChaptersMaths and Art: Kissing CousinsUsing Equations to Draw HandsDrawing to Understand Mathematical ConceptsUse Maths to Learn How to DrawMaths: Indispensable for Perspective DrawingThe Final Word is PhiAre you a right brained, creative type?If so, learning how to draw gives you another creative outlet; another reason to daydream and keep your head in the clouds.Which means you don't have much patience or aptitude for dry-as-sticks subjects like maths... right?If that is the case, you might be surprised to learn that maths and art are intimately intertwined!Proportion, symmetry, the ratio of light to shadow in each piece; dimensions, perspective and gradients of color: the vocabulary of art is the language of maths!Let us now delve further into the similarities â€" and differences of these two disciplines.Maths and drawing are kissing cousins! Source: Pixabay Credit: Bess HarnitiEven negative space has a place, both in art and in maths!The shared values of abstract versus figurativ e art, at the junction at where they intersect: their common denominator is maths. Another reason to learn to draw, and a new reason to rediscover maths!Using Equations to Draw HandsYou might know of the the fellow across the pond named Jason Padgett. He was grievously injured one night, after karaoke and, when he woke up, he discovered he saw the world through an intricate filter of  geometrical patterns.Prior to that, he was quite happy as a furniture salesman with no desire to even consider the shape of furniture, let alone drawing any.We do not encourage getting beaten into savant syndrome to gain the same perspective as Mr. Padgett.Instead, you could just enjoy his geometric patterns, most drawn in a one point perspective.Here is a bit more on the unique Mr. Padgett, who before had never had the faintest interest in anything academic, let alone maths.He started drawing what he was seeing and, curiously enough, he attracted the attention of the scientific community.The consensus : everyone unanimously agrees that every bit of his line drawings and other renderings were geometrically accurate and depict mathematical equations.Today, this amazing artist continues to draw mathematically satisfying   artistic equations that are the envy of every geometry professor.For many of us, his work remains among the finest expressions of symmetrical art.Surely you know of the premier example of such?It would be Da Vinci's Vitruvian Man, a pen and ink on paper, which, incidentally is the basis for validation of the value phi, also known as the perfect proportion or the golden ratio.Whether through art or maths, learn what jobs you can land if you can draw...Start drawing better by taking the new drawing lessons here.Can you spot the horizon line in this landscape? Source: Pixabay Credit: ManeeG place it in perspective to the horizon. And then, note the rising sun: how does it relate to the cottage and the horizon line?And, just like that, you have created a one point pers pective in your mind!Hopefully, you will have your sketchbook handy; these geometric revelations don't happen at the drop of the hat!Unless your name is Jason Padgett, of course. The Final Word is PhiIn all of your drawing tutorials, as you hone your drawing skills; while you charcoal your next still life or use Conté crayons to add textures and light shade... Whether you know it or not, every figure drawing you have rendered is driven by phi (pronounced fee). This is the golden ratio we mentioned before; the one that Leonardo da Vinci was so obsessed over that he reputedly dug up freshly buried cadavers  for dissection, study and measurement. Consciously or not, everyone who is any kind of an artist, from cartoonist and manga to portrait painter and architect, seeks to find and recreate this mathematical value in art simply by following their artistic sense. We find the golden proportion in the columns of the Parthenon, and the structures of Le Corbusier and Frank Lloyd Wright.Gra phic designers have appropriated this perfect proportion, that you will find among the most famous company logos, in particular the famous apple's Apple. Not to mention the National Geographic logo. You know, the yellow rectangle, hard to make simpler ... It is not only yellow, it is also a golden rectangle!With phi all around us, it is easy to see how maths influences art.  Or is it the other way around?

Top Five Things To Look for In An Online Algebra Tutor

Top Five Things To Look for In An Online Algebra Tutor Maths is always a matter of concern for maximum parents. Students generally develop a phobia for the numbers and it becomes more traumatic for students when alphabets are added onto them in the middle school. Get help of online algebra tutor to overcome this fear. There are very less number of pupils who actually enjoy this section of maths. Even if the students have a lending hand for homework, maths often becomes a problem for them. This is because; this particular subject needs some definite logic behind making it understandable. It would be beneficial for the student if he/she gets a good guidance from a professional. These numbers with alphabets often become nightmare for students. Therefore, the parent must appoint a perfect professional in this field to make it beneficiary for the student. However, the parents must keep in mind before appointing them for their kids. How To Sort And Solve Elapsed Time Story Problems http://t.co/j3zGC5Q6m8 #algebra #backtoschool #homeschool pic.twitter.com/dzdb9M73Rl â€" Tutor Pace (@TutorPace) August 4, 2015 Why parents should opt for online algebra tutor? In this rush of knowing everything, students are also over-scheduled with their tasks. Regular classes in school with extracurricular activities, any child does not really have a quality time to study. But, unfortunately one has to run to be successful in the near future. An online algebra homework help can be very beneficial for students in mid school. There are certain aspects that need to be kept in mind before appointing an online tutor. The First Ladder To Success In #Algebra Is Right Tutor http://t.co/WHQqrujiah #backtoschool pic.twitter.com/RyHhluTBVn â€" Tutor Pace (@TutorPace) September 2, 2015 Five such important points are: The teacher should have a background on maths or science and not any other arts major. You also need to find out whether the teacher has any definite experience or not on being a  online algebra tutor. All the more, it should be noted whether the teacher has fine techniques of teaching. However, many teachers holding big degrees in maths and having done specialization on algebra may not be of great help to the students. Whereas, somebody who knows the basics of algebra can make a student absolutely phobia less in this subject for the rest of their lives. The teacher should also be flexible in changing their techniques while teaching. These online tutors are also handy for the college students who are doing a specialization paper on algebra. They may appoint a good professional for algebra assignment help. They can be guided for their assignments, dissertation papers and for seminars through these online tutors. The next point is to note whether the teacher has right access to online teaching. The tutor should have advanced software to be accessible to students. Will they be able to conduct online tests? Will they be accessible when the student needs help with his/her homeworks? Or whether they can provide your child with proper chat room that may help in the learning process etc.? There should also be safety assurance from the tutor to the child. Parents should be properly acquainted with the background of the teacher before the teacher comes in contact with the child. There are also rules where the parents can undergo solid character check before appointing them for the students. The fees that becomes the major issue in these online courses, needs to be handled carefully. There are many such fraud cases that gets reported with the names of online teaching. Therefore, the students , if matured enough and understands the online payment procedures should handle it very carefully only after getting proper authentication. If they are unable to understand that, they may take the help of their parents to ensure a secured payment.

What To Know About The Writing Section Of The ACT

What To Know About The Writing Section Of The ACT The ACT Plus Writing includes an optional supplement to the standard exam. The half-hour test assesses your writing skills especially those writing skills emphasized in your high school English courses and in entry-level college composition classes. Well go over if you should register to take the additional Writing Test, what the prompt looks like, how to optimize your exam grade, and exactly what the ACT scorers are looking for when they read your essay. If you think you need additional assistance, you may want to contact an ACT tutoror review an ACT prep book.What does the Writing Test look like? The writing portion of the ACT gives a single prompt that describes an issue and the opposing points of view on the subject. You will be asked to state your position and adopt one or more of the stances described in the question. Your score will not be affected by your viewpoint.Since the Writing Test is optional, do I actually need to take it? It depends on where you are applying. Some c olleges and universities have decided to either require or recommend their ACT-taking applicants (as opposed to the SAT) opt for the Writing Test. Others have decided that Writing Test scores are not necessary. In other words, you should decide if you want to take the writing portion based on the requirements of the colleges to which you are applying. For example, Princeton and Yale both require the ACT Plus Writing, while Notre Dame and Johns Hopkins University recommend it, and Georgetown University has decided the supplement is not needed altogether. If you are planning on applying to multiple schools, contact the admissions office or check online to find out their preferences when it comes to the writing exam. Even if they do not require it, most colleges will accept scores from the ACT Plus Writing.But my dream school doesnt require the Writing Test. So do you really, really need to sit through another 30 minutes of the ACT? Unless you think youll do terribly, its safest in the long run to take the writing exam in case you change your mind, apply elsewhere, or are not accepted to your first choice school. If youre planning on applying to school(s) that dont require the writing supplement, but change your mind and decide to apply to one that does, you wouldnt want to have to retake the entire ACT just to include the Writing Test. That said, its best to take the ACT Plus Writing so you are not limiting yourself in the college admissions process. Does it matter when I take it? It actually doesnt - the ACT Plus Writing exam is offered on all national test dates in the United States, US territories, Puerto Rico, and Canada. It is also available on four international test days in other areas, and for Special or Arranged Testing.Does taking the ACT Plus Writing affect the price? Yes. Taking the standard ACT (with no writing) is $34 and taking the ACT Plus Writing is $49.50. The extra price tag includes score reports for up to four colleges when you list a valid code when you register online. However, the extra $15.50 writing exam fee is refundable on request if you are absent or decide to take the standard ACT (with no writing) before test day. What exactly am I being scored on? The ACT raters have a set of criteria that they use to judge each individual essay. Grades are given based on how well you articulate your perspective, use supporting evidence and logic, and maintain an emphasis on your position throughout the essay. Your ability to organize ideas logically and how well you communicate your argument through writing are also judged. How can I optimize my score? Make sure you understand the prompt and the issue at hand its okay to take another minute and reread the question. Be careful when picking a stance and remember that you dont necessarily have to take the position you believe. Instead, argue the perspective that you can give the best evidence for.Before beginning, use your Writing Test booklet to jot down some notes, organize your essay or create a brief outline. Brainstorm some reasons and examples you can use to explain your point of view on the topic. Keep in mind how others could respond to your viewpoint and how you could disprove their arguments. Spending a few minutes planning the layout of your essay ahead of time will help keep you on track and organized while youre writing. In your introduction, explain the issue and your position in a clear and rational way. In the next paragraph or two, elaborate on the topic in a larger context or describe the implications and why it is especially problematical. Be persuasive and address how those in opposition could respond to your viewpoint and provide a convincing counterargument. Stay focused on the subject and present specific examples. Your essay will be stronger if you clarify logical relationships by employing transitional phrases and words, varying sentence structure, and using precise and diverse word choices. Wrap up your essay with a powerful co nclusion that summarizes or reinforces your argument.Time is short on the Writing Test, so make the most of the 30 minutes. While you may also use ACT practice teststo prep for the rest of the exam, don't forget to prepare accordingly for this portion as well. On the test, remember to recheck your work before time is up, and fix any errors in grammar, punctuation, or spelling, and make sure that all words are easy to read.

4 Tactics for Landing Your Dream Job

4 Tactics for Landing Your Dream Job The following is a guest post written by Caitlin Grove, an Associate Content Coordinatorfor Varsity Tutors. When you start to see the light at the end of the college tunnel, one particular question may cross your mind: How do I land my dream job? The idea of exiting the college journey and moving directly to your dream career is enticing. The harsh reality is that it isnt a simple process. Before I landed my current position as Associate Content Coordinator with Varsity Tutors, I had to be honest with myself about what the term dream job meant for me and how I would ultimately get there. In some ways, securing your dream job is like apartment hunting. Youve likely lived in several places by now, and you know what your must-haves are. You also know your criteria for your dream job. If youre confident in your vision for a fulfilling career, dont settleinstead, take these four steps to land your dream job. 1. Attend recruitment events at your dream companies Chances are youve wondered what it would be like to work at your dream company or companies, but short of securing an employment offer, how can you find out? In two words: recruitment events. Companies often host recruitment events like open houses for potential employees, sometimes in their headquarters or in a local office. These events give you the opportunity to decide if a companys mission, vision, and culture are right for you. The organization's culture, or the values and behaviors of the workplace environment, will be a significant factor in whether or not a particular job is right for you. Personally, I was looking to work for a company with a collaborative and supportive culture after I graduated college, which is exactly what I found in my current role. Realize that you might love a company based on its social presence or products, but the culture might be a negative environment to work in. Be honest with yourself about this aspect when attending recruitment events. Its important to consider these events mini-interviews. Dress professionally, research the company in advance, and prepare a short list of key qualities you possess that will make you a great fit for the organization. In short, come equipped with your elevator speech. Use this time to showcase why you mesh with the company's culture and brand. 2. Use social media as a networking tool The same social media accounts that you use daily can play a part in landing your dream job. As you likely know, social media is a great platform for connecting with others, including those individuals who work for your dream company or companies. Maintain a professional, active presence on your social channels to illustrate what you bring to the tableaim to post relevant and engaging content several times per week. On LinkedIn, join groups in an effort to connect with like-minded individuals in your field. Start a conversation on Twitter by commenting on or retweeting posts that are relevant to your desired profession. You can also join arranged Twitter conversations (or Twitter chats). When it comes to networking on social media, you can establish a rapport with individuals in your field with just a bit of effort. So long as you are contributing value to the conversations you enter or begin, networking through social media can help you land your dream job. Keep in mind, however, that while social media can be a great way to network, it can have a negative impact on your job search if used incorrectly. [RELATED: What College Students Should Know About Social Media] 3. Review your current skill set What skills and knowledge are central to your dream job? Do you confidently possess these attributes? Now is the time to ask yourself these questions, and, if necessary, find ways to improve your dream job toolkit. My current position, for example, requires copy editing skills and familiarity with Adobe InDesign and Photoshop. While in college, I chose classes (like Writing for the Corporate and Institutional Market) and on-campus jobs that would help me build these skills before graduation. I also surrounded myself with professors and classmates who could provide support. For instance, if you have a friend whos a computer science major and you want to strengthen your coding skills, see what they can teach you. Keep in mind that you dont have to be outstanding in every single skill required by your dream job. The important thing is to showcase that you have a base level of knowledge and the drive to continue learning new skills once you begin employment. [RELATED: 4 Career Skills for Students to Develop] 4. Gain experience in your desired field prior to graduation Youre probably attending college with the end goal of pursuing a specific career, so why not show your future employer just how serious you are about the field? You can gain experience in your desired field via internships, on-campus jobs, research opportunities, and volunteer positions. [RELATED: How to Get Real-World Experience in Your College Major] These types of experiences can help you immensely when attempting to secure your dream job. They can put you in contact with industry connections, help you develop new skills, and demonstrate that you have real-world experience in your dream job. If you are still committed to your dream companies after attending recruitment events and networking with individuals within the organizations, pursue internships at those businesses. This can be a great way to get your foot in the door and to further discover if this is the right position and company for you. Use this experience, along with the other efforts described above, to illustrate to potential employers why you deserve your dream career. Any topics you want to know more about? Let us know! The Varsity Tutors Blog editors love hearing your feedback and opinions. Feel free to email us at blog@varsitytutors.com.

Popular English Christmas Idioms and Sayings ?? - Upgrade your English

Popular English Christmas Idioms and Sayings ?? - Upgrade your English Christmas is the most popular holiday celebrated in the UK. There are lots of customs and traditions including nativity plays, decorating our homes, singing carols and having a traditional roast turkey dinner on Christmas day. Here are some popular English Christmas idioms and sayings that can be used during the holiday season. 11 English Christmas Idioms and Sayings Christmas comes but once a yearAs it only happens once a year we should treat people less fortunate than us a bit better in the Christmas season.Example: Jane went to the charity shop and made a large donation of cash for the homeless people. After all Christmas only comes once a year.To cancel someones ChristmasWhen a person threatens to cancel someones Christmas, it means he/she wants to kill or destroy someone (not literally, of course!) as the dead person will miss Christmas.Example: If Sam keeps bugging me, Im going to cancel his Christmas this year. All my Christmases have come togetherTo experience an event of extreme good luck or happiness, something happened that you were dreaming about.Example:  Last week I received an amazing job offer and yesterday my boyfriend proposed to me! It feels like all my Christmases have come together.To light up like a Christmas treeSomething had a dramatic effect on someones mood. Some event or situation made someone very happy.Example: Sarah saw a box of chocolates on her desk, and she lit up like a Christmas tree. Eat, drink and be merryEnjoy yourselves with good food and drink.Example: Welcome to our party! Eat, drink and be merry.Trim the treeto add decorations to the Christmas tree like ornaments, ribbons, baubles, or lace.Example: It was a longterm tradition for the whole family to trim the tree together.White elephanta gift exchange in which people bring unwanted itemsExample: Where did you get that ugly vase? Oh, I got it at a white elephant at work.Pigs in blanketsA variety of sausage-based foods in the UK, USA and Ireland. In the USA pigs in blankets are small sausages wrapped in croissant rolls.In the UK the ‘blanket’ is bacon. Pigs in blankets are a perfect   accompaniment to the traditional Christmas dinner. 11 English Christmas Idioms and Sayings Like turkeys voting for ChristmasTurkeys are the favourite choice of food for the Christmas dinner. When people accept a decision which is not going to work out well for them it is like turkeys voting for Christmas.Example:  The teachers agreed to accept the introduction of larger class numbers without any increase in their pay. It was like Turkeys voting for Christmas.To ring in the New YearTo have a party on New Year’s Eve (31st December) to welcome the New Year. When the church bells ring everyone wishes each other a happy New Year.Example: May and Christopher invited their friends to their home for a New Year’s Eve party to help them ring in the New Year.Christmas has come earlySomeone gets a welcome surprise they were not expecting.Example: Jonathan got a letter from his boss on the 1st December telling him that he had been promoted and was to receive a bonus. Indeed Christmas had come early for him.Bah, HumbugEbenezer Scrooge, the main character of Charles Dickens novel Chr istmas Carol used this term quite often. This expression is often used in the context of someone who shows a lack of Christmas spirit and ruins  other peoples enjoyment.

More Idioms Associated with Our Body Parts - Intermediate Level English

More Idioms Associated with Our Body Parts - Intermediate Level English In the last blog we learned about English idioms related to body parts. There are many such sayings in the English language so I thought I might follow up and teach you some further English phrases and idioms associated with our body parts. More Idioms Associated with Our Body Parts A HAND IN ITTo have a hand in  something usually refers to you having a part to play in something.Michael was praised for signing up a very large new client account but he told his manager that Mary had a hand in it too and was also responsible for landing this client.LOSE YOUR HEADUsually used when someone gets very angry over some issue and becomes very annoyed. John was told that he was losing his job even though he had performed very well recently.He confronted his manager and lost his head  completely and called his manager some very bad names.TO PUT YOUR TOE IN THE WATERWhen you decide to attempt something perhaps for the first time and decide to do it gradually or slowly until you are more comfortable about it.They asked him to invest some money in a new business. He thought it sounded a good idea but did not want to risk a lot so he decided to put his toe in the water  and invest a small amount initially until he understood it better.TO STICK YOUR NOSE INWhere there is perhap s an argument or an incident that has nothing to do with you, you still decide to get involved and offer your opinion. In such a situation you are said to be sticking your nose in to someone else’s business.TO POINT THE FINGER ATIf you know or believe you know who is responsible for or guilty of a crime you  point the finger at  that person.He was the last one to see her alive. The finger of blame was pointed at  him immediately. Body Parts English Idioms - Infographic Enjoyed this infographic? Here’s what you can do next: TURN A DEAF EARrefuse to listen to someoneWhen I applied for this position, they turned a deaf ear on me. No updates, no phone calls, nothing for days. EAT THE HEAD OFF SOMEONEto speak angrily or rudely to someone or to be very abrupt with someone. You can also use TO BITE ONES HEAD OFF with the same meaning.My boss nearly ate the head off me on Monday morning as I forgot to run an important report.TO PUT ONES FOOT IN ONES MOUTHto embarrass oneself by ssaying something foolish, inappropriate or even offensivePaul often  puts his foot in his mouth by  speaking before thinking.  FOOT THE BILLhaving to pay the bill when somebody does something but doesnt have the money to pay for itLast year Sarah broke her arm and her insurance refused to cover the costs so had to foot the bill herself.TO HAVE YOUR HEART IN YOUR MOUTHto very nervous or frightenedSarahs husband drives like a maniac. I had my heart in my mouth all the way to Dublin.TO GIVE SOMEONE A PIECE OF YOUR MINDto scold someone sev erely; to tell someone angrily what you think of themWhen she found out that he hadn’t done what he had promised to do, she really gave him a piece of her mind.LET YOUR HAIR DOWNto behave in much more freely way than usual, to enjoy oneself, to have a good timeIts Friday! Lets let our hair down and have some fun.

Happy Holidays and a Successful School Year 2015!

Happy Holidays and a Successful School Year 2015! Joy Joy Joy! TutorZ delivers the warmest wishes for a wonderful Holiday Season and a successful start of the 2015 school year to all of our tutors, teachers, instructors, parents and students. We are sincerely delighted to have you as our customers. We are wishing you a holiday season filled with peace and joy. May bright ideas and new insights greet you each day of the new year. We also hope that your beautiful wishes for 2015 come true and you achieve your educational targets. If we can help you to reach your goal come back in 2015 to get more tutoring at TutorZ. Happy holidays and lots of reasons to smile!