Solve a quadratic equation by factorising

﻿Hi, my name's Mr. Clasper, and today we're going to learn how to simplify an algebra fraction by factorising. Let's begin with a recap on simplifying fractions. We need to simplify 12/18. So one way to do this, is to find a highest common factor, in this case, the highest common factor of 12 and 18 is six. And if we divide the numerator and the denominator by six, that leaves us with 2/3. Now, another way to think about this is to rewrite the fraction as six multiply by two all over by six multiplied by three, which would still be equivalent to 12/18. And another way to write this would be 6/6 multiplied by 2/3. Now, if we look carefully, we can see that 6/6 would actually simplify to one whole, which means that that is equivalent to a calculation of one multiplied by 2/3. However, anything multiplied by one is always itself. Therefore again, proving that 12/18 is equal to 2/3. Let's simplify this fraction. We could write this as a multiplication of two separate fractions. And if we look carefully because the second fraction has the same value in the numerator, as it does the denominator, this would have a value of one. That means that we can cancel these two out. And that leaves us with y plus three, all over y plus eight, which is our simplified algebraic fraction. Let's have a look at another example. We could take our fraction and write it as a multiplication again, this time we would have our fraction over one, multiplied by y plus five, all over y plus five. And again, looking at the second fraction, this fraction has a value of one. Therefore, we can cancel this out and that would leave us with y plus three, all over one. We could also write this as y plus three. Let's try one more example. We could write this as a multiplication and yet again, the second fraction has the same value in the numerator as it does the denominator. Therefore it must equal one and we can cancel these out. That would leave us with one over y plus two. Here are some questions for you to try, pause the video to complete your task resume once you're finished. And here are your answers. If we look at 1 , we get an answer of one over m plus five. So we don't just get m plus five as that would be incorrect. And for 1 we get w plus two, if you've written w plus two over one, that is equivalent, but generally speaking, we don't need to write that division of one in this case. So w plus two will be better. Let's simplify this fraction. Before we can start we need to make sure that we factorise the numerator. Factorising the numerator will give us y plus three and y plus four. That means our new numerator can become y plus three and y plus four. And again, following the same process, if we look carefully, we can see that the numerator and the denominator both have a factor of y plus three. So dividing these two would give us a value of one, therefore we can cancel these out. That leaves us with y plus four, all over y plus two. Here are some questions for you to try, pause the video to complete your task, resume once you're finished. And here are your answers, just be careful with part . So when we factorise our numerator, we should get d plus one and d minus 10. And then we discover that the denominator also has a factor of d plus one, which means we get our simplified answer of d minus 10, all over d plus one. Here are some questions for you to try pause the video, to complete your task and resume once you're finished. And here are your solutions. So let's take a look at each of these. We have 3 the mistake was that the numerator should actually factorise to a minus two all multiplied by a plus three. And this would give us a final answer of a plus three, all over a plus five. If we take a look at part , the final answer should be one over b minus five, not just b minus five, as this has a different value. And for part , this should actually factorise to c minus six, all multiplied by c plus six. This has because c squared minus 36 is a difference of two squares. That being said, if we factorise correctly, we would get a final answer of c plus six and c plus three. And that is it for our lesson. I hope you've enjoyed it. Hopefully see you soon.

Simplifying an algebraic fraction by factorising

In this lesson, we will learn how to simplify algebraic fractions by factorising and identifying common factors in both the numerator and denominator.

Lesson overview:Simplifying an algebraic fraction by factorising

Core Content

Factorise and solve a quadratic (a=1):