Simplifying Algebraic Fractions

Here we will learn about simplifying algebraic fractions, including different powers of x , quadratics, and the difference of two squares.

There are also simplifying algebraic fractions worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is simplifying algebraic fractions?

Simplifying algebraic fractions is simplifying a fraction that contains algebra so that the numerator and the denominator do not contain any common factors.

To do this, we need to be able to find common factors between the numerator and the denominator which can be cancelled down.

In order to simplify algebraic fractions, you must be confident with calculating with fractions.

The general form when adding fractions is:

The general form for subtracting fractions is:

So if a = 2, b = 5, c = 1 and d = 4 , we can therefore say that

Below is a visual representation of this problem,

By converting the fractions so that they have a common denominator (in this case 20 ), we divide the fractions into smaller parts, then total those parts, all by using knowledge of equivalent fractions.

We can use this to simplify algebraic expressions:

E.g.
Let’s look at \frac

Here, the terms 5x and 15 share a common factor of 5 .

If we wrote this out as two products, we would get \frac>> .

We can simplify this by cancelling the common factor of 5 from the numerator and the denominator of the fraction \frac>>=\frac .

So by finding the highest common factor of the numerator and the denominator, we can show that the fraction \frac can be expressed as as the more simple algebraic fraction \frac .

We can use knowledge of simplifying algebraic fractions to solve equations that include algebraic fractions. For more information on this, see the lesson on algebraic fractions.

Step-by-step guide: Algebraic fractions