Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to be solving algebraic fraction equations that involve an addition or a subtraction.

In this example, we need to complete the addition before we begin to solve the equation to find the value of y.

The lowest common denominator of this pair of fractions is four.

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

This gives two y add six divided by four.

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

Next, we can multiply both sides of the equation by four.

This gives three y add seven is equal to 40.

We can next subtract seven from both sides and then divide both sides of the equation by three to give y is equal to 11.

Here are some questions for you to try.

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

Here are the answers.

You should have completed the addition or subtraction before you solved the equation.

With this next example, we need to complete the subtraction before we solve the equation to work out the value of b.

The common denominator of these two fractions is b subtract three multiplied by b subtract two.

We're going to multiply both the numerator and the denominator of the first fraction by b subtract two, and the second fraction, we're going to multiply both the numerator and the denominator by b subtract three.

Next, we need to expand the brackets of both of the numerators of the fractions.

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

Negative eight subtract negative nine is equivalent to negative eight add nine.

Both of these calculations give an answer of positive one.

Next, we're going to multiply both sides of the equation by b subtract two multiplied by b subtract three.

Then, we're going to expand this bracket.

We need to make this equation equal to zero to be able to solve it, as it is a quadratic.

To do this, we're going to subtract b from both sides and then subtract one from both sides.

We can now factorise the right-hand side of this equation.

So b is equal to one or b is equal to five.

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.

For question three, you should have two solutions for each equation.

This is because quadratic equations mostly have two solutions.

That's all for this lesson.

Thanks for watching.