GlossariesGCSE GlossariesGCSE Maths GlossaryAlgebraic Fraction

Algebraic Fraction - GCSE Maths Definition

Reviewed by: Dan Finlay

Last updated

13 May 2025

What is an algebraic fraction?

In GCSE maths, an algebraic fraction is a fraction where the numerator and/or denominator contain an algebraic expression. Here are some examples of algebraic fractions:

$\frac{2}{x + 1}$
$\frac{2 x + 3}{x + 1}$
$\frac{x^{2} - 1}{x - 1}$

Algebraic fractions follow the usual rules of numerical fractions.

To simplify algebraic fractions, cancel out common factors from the numerator and the denominator.	$\frac{(x + 1) (x - 3)}{(x + 1) (2 x - 5)} = \frac{x - 3}{2 x - 5}$
To add or subtract algebraic fractions, find equivalent fractions so that both fractions have a common denominator.	$\frac{2}{x} + \frac{x - 2}{x + 1} = \frac{2 (x + 1)}{x (x + 1)} + \frac{x (x - 2)}{x (x + 1)} = \frac{2 (x + 1) + x (x - 2)}{x (x + 1)}$
To multiply algebraic fractions, multiply the numerators together and multiply the denominators together.	$\frac{x}{x + 1} \times \frac{x - 1}{4} = \frac{x (x - 1)}{4 (x + 1)}$
To divide algebraic fractions, multiply the first fraction by the reciprocal of the second fraction.	$\frac{x}{x + 1} \div \frac{x - 1}{4} = \frac{x}{x + 1} \times \frac{4}{x - 1} = \frac{4 x}{(x + 1) (x - 1)}$

Examiner-written GCSE Maths revision resources that improve your grades 2x

Written by expert teachers and examiners
Aligned to exam specifications
Everything you need to know, and nothing you don’t

GCSE Maths revision resources

Related GCSE Maths glossary terms

Angle of depression: GCSE Maths Definition
Dan Finlay, Maths Subject Lead

Share this article

Algebraic Fraction - GCSE Maths Definition

What is an algebraic fraction?

Reviewer: Dan Finlay

The examiner written revision resources that improve your grades 2x.