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Hi, my name's Mr. Clasper, and today we're going to learn how to simplify an algebraic fraction, by factorising quadratics.

Let's simplify this fraction.

One way to view this, is to think of it as a multiplication, of two fractions.

If we look carefully at the second fraction, we can see that the numerator and the denominator have the same value.

Therefore these would equal one.

That means that 3y plus seven, is a factor of both the numerator and the denominator, therefore we can cancel these out.

This means that when we simplify our fraction, we get Y plus, all over 3y plus eight.

Let's try a different example.

So we could write this as a product of these two fractions.

And again, if we look carefully at the second fraction, as the numerator has the same value as the denominator, we can cancel these out, as they have a value of one.

This means that when we simplify our fraction, we get a value of Y plus three, all over one.

Which could also be written as Y plus three.

Let's try this example.

Again, we could write this as a product of two fractions.

And if we look at our second fraction, Y plus three, all over Y plus three, would give a value of one.

Therefore we can cancel this out.

This would leave us a value of one, over four Y plus two.

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 answers.

If we look carefully at question 1c, we should get one over M plus five, so there shouldn't just be M plus five.

And for 1d we should get 3w plus two.

If you've written 3w plus two over one, that is equivalent, but it's better if you can write it as 3w plus two.

Let's simplify this fraction.

Before we begin, we need to factorise the numerator.

If we factorise our expression, we would get 2y plus three, multiplied by Y plus two.

This means that our original fraction, is equivalent to 2y plus three, all multipied by Y plus two.

All over, Y plus two, multiplied by Y plus three.

Let's simplify that fraction.

So, looking at this fraction, we can see that the numerator and the denominator both have a factor of Y plus two.

So that means when these are divided by each other, they will give a value of one, or cancel out.

This means that our simplified fraction would be, 2y plus three, all over, Y plus three.

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 answers.

So just make sure that you factorise any expressions which can be factorised, as this helps our process.

And if we take a look at D, when we factorise the numerator and the denominator, we would find a common factor of 2d plus one in both the numerator and the denominator.

So therefore these would cancel out, and leave us with D plus five, all over D minus one.

Here is our last question.

Pause the video to complete your task, and resume once you're finished.

And here are the solutions.

If we look at the first statement, we can see that A plus three is actually the common factor, therefore, it's this that needed to be cancelled out, leaving us with 2a plus one, all over 2a minus one.

If we look at part B, we can see that the correct answer should be one over 2b plus one.

And looking at part C, we actually have a difference of two squares in our numerator.

This means that when we factorise, we should get 2c plus five, and 2c minus five.

So when we simplify this and find our common factor in the numerator and denominator, they should leave us with 2c plus five, all over C plus three.

And that brings us nicely to the end of our lesson.

I hope you've had fun simplifying fractions, and I will hopefully see you soon.