Cancelling Algebraic Fractions

This chapter explores cancelling algebraic fractions. It covers cancelling down algebraic fractions including brackets.

Simplifying 15ab divide by 3ab

When working with algebraic fractions you will sometimes have to cancel the top with the bottom. Suppose we wanted to work out.

To make this simple for yourself we would have to expand the fractions and work it out in parts for example a² = a x a. Below we’ve expanded the fractions;

You can see that we have as and bs on top which correspond with those in the bottom. Here we simply cancel those out. Let’s start with the bs;

There is more letters which can cancel out. The as can cancel out as well.

That leaves;

15 can divide with 3, so we can cancel this as shown below;

This leaves the answer as;

Simplify 3a+6 divide by 5ab

Suppose we wanted to simplify;

First we factorise the expression above. The above expression is quite vague, it appears like we can cancel down the as as it is but we could not and cannot. First we need to factorise the top part, we know that 3a+6 factorises to 3(a+2) If you don’t know how to factorise you can search factorising in the search box above. So the fraction becomes;

Now you might realise that we can cancel out the 3s as shown below;

So the final answer for this division becomes;

Simplify 4ab + 8a divide by 12a

Again with this problem, we have to factorise the numerator first. 4ab + 8a² becomes;

Now we can cancel out as shown below;

Notice the top and bottom are multiples of 4 so we can reduce these as shown below;

That leaves;

Simplifying 2x + x – 3 divide by x – 1

Suppose we wanted to divide;

The division above is not different to the one above. In this variation we have to factorise both the numerator and the denominator as shown below;

Here what needs to be cancelled out becomes very clear;

What remains as the answer becomes;