Lesson video

Hi, I am Miss Davis.

In this lesson, we're going to be writing the difference of two algebraic fractions.

What's the same and what is different about these calculations? We can see that the numerators are the same.

Seven is a factor of 28.

We multiply seven by four to get to 28.

A is a factor of 4A.

We multiply A by four to get 4A.

We're going to multiply the numerator and the denominator in this first fraction by four.

We're going to do this in the second example as well.

Now that the denominators are the same, we can complete the subtraction.

Subtracting algebraic fractions works in the same way as adding numerical fractions.

We're going to simplify this expression.

B is a factor of BC.

So our common denominator is BC.

We're going to multiply both the numerator and the denominator of the second fraction by C.

Now that the denominators are the same, we can complete the subtraction.

Five and negative 8C are like terms. This fraction cannot be simplified any more.

Let's have a go at this next one.

E is a factor of E squared.

Going to multiply both the numerator and the denominator of the second fraction by E to make the denominator E squared.

This gives us 11 E over E squared.

Now that the denominators are the same, we can complete the subtraction.

In our final example, 2X is a factor of six ST.

We're going to multiply two S by three T to make the denominators the same.

We're going to multiply one by three T as well.

This gives three T over six ST.

We can now complete this subtraction, as the denominators are the same.

This can't be simplified at all, so this is our final answer.

Here are some questions for you to try.

Pause the video to complete your task, and resume when you finish.

Here are the answers.

In all of these questions, one denominator is a multiple of the other.

This means that you only need to multiply the numerator by the denominator of one of the fractions.

We're going to simplify this expression.

C subtract seven is a factor of three C subtract seven.

We're going to multiply the numerator and the denominator of the first fraction by three.

This gives us 42C over three bracket C subtract seven.

Because the denominators are the same, we can complete the subtraction.

In this next example, E subtract P is a factor of E subtract P squared.

The common denominator is E subtract P squared.

We're going to multiply both the numerator and the denominator of the second fraction by E subtract P to make the denominators the same.

This gives 11 lots of E subtract P divided by E subtract P squared.

Before we can complete this subtraction, we need to expand the brackets of the numerator in the second fraction.

We can now complete the subtraction.

In this next example, our denominators are not factors of the other.

Our common denominator is going to be S subtract five multiplied by S subtract three.

We're going to make the denominators the same.

To do this, we're going to multiply both the numerator and denominator in the first fraction by S subtract three.

And the second fraction, we're going to multiply both the numerator and denominator by S subtract five.

Next we're going to expand the numerators of both fractions.

We can then complete the subtraction.

This cannot be simplified, so it is our final answer.

Here are some questions for you to try.

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

Here are the answers.

Leave the denominators in their factorised form.

This will make it easier if you need to simplify any answers.

Here are some questions for you to try.

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

Here are the answers.

You should be leaving your denominator in their factorised forms. This means that if you ever have to simplify, it's just easier to identify this.

That's all for this lesson.

Thanks for watching.