Lesson video

Hi I'm Ms. Davis.

In this lesson we're going to be writing the sum of two algebraic fractions where the denominator is an expression.

What's the same and what's different about these calculations? The numerators are the same.

In the first example, 7 is a factor of 35.

In the second example, a is a factor of a.

We're going to multiply the first fraction by 5.

In the second example, we're going to multiply both numerator and denominator of the first fraction by 5.

The calculations work in the same way with both examples.

Let's have a go at this example.

b is a factor of bc.

So we're going to multiply both the numerator and the denominator in this second fraction by c.

This would give us 8c over bc.

Now that the denominators are the same, we can add the numerators together.

Is it this? No.

7 is not a like term with 8c.

So we can't add those together.

As this can't be simplified, it is our final answer.

Let's look at this next example.

e is a factor of e squared.

So we're going to multiply both the numerator and denominator of the second fraction by e.

This gives us 11e over e squared.

Now that the denominators are the same, we can add the fractions together.

This gives us 4 add 11e all over e squared.

This can't be simplified so it is our final answer.

Let's have a look at this last example.

2s is a factor of 6st.

We would need to multiply both the numerator and the denominator by 3t.

This would mean that the denominator is 6st and the numerator is 3t.

We can now add these two fractions together as the denominators are the same.

Because this can't be simplified it is our final answer.

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.

In these questions one of these denominators is a factor of the other.

Here is a question for you to try.

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

Here are the answers.

Susie didn't multiply the numerator of the first fraction the same way she did with the denominator.

Let's have a look at this next example.

The first denominator is c add 1.

The second denominator is 6 bracket c add 1.

This means that our common denominator is 6 bracket c add 1.

We need to multiply both the numerator and denominator of the first fraction by 6.

As the denominators are now the same, we can add these two fractions together.

You can leave the denominator in a factorised form.

With this next example, e add 2 is a factor of e add 2 squared.

The lowest common denominator is e add 2 squared.

We need to multiply both the numerator and the denominator of the second fraction by e add 2.

We need to expand the second numerator.

We can now add the numerators together, as the denominators are the same.

This is our final answer.

In our final example, we do not have denominators that are a factor of another.

To complete this addition we need to find the lowest common denominator.

This will be s add 5 multiplied by s subtract 3.

We're going to multiply this first fraction both the numerator and the denominator by s subtract 3.

Then we're going to multiply the numerator and the denominator of the second fraction by s add 5.

We need to expand the numerators of both fractions.

The first numerator will become s squared subtract 2s subtract 3.

Second numerator will become s squared add 5s.

We leave the denominators in their factorised form.

This simplifies to 2s squared add 3s subtract 3 all divided by s add 5 multiplied by s subtract 3.

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.

Leave denominators in their factorised form.

As this makes it easier if you need to simplify.

Here is a question for you to try.

Pause the video to complete your task.

And resume once you're finished.

Here is the answer.

A linear sequence goes up or down by the same amount between each term.

To work out this third term you needed to do 2 over t add 1 add 9 over t add 4.

That's all for this lesson thanks for watching.