### Introduction

Just as one whole number divided by another is called a numerical fraction, so one algebraic expression divided by another is known as an
**
algebraic fraction
**
. Examples are

$\phantom{\rule{2em}{0ex}}\frac{x}{y},\phantom{\rule{1em}{0ex}}\frac{3x+2y}{x-y},\phantom{\rule{2em}{0ex}}\text{and}\phantom{\rule{2em}{0ex}}\frac{{x}^{2}+3x+1}{x-4}$

In this Section we explain how algebraic fractions can be simplified, added, subtracted, multiplied and divided.

#### Prerequisites

- be familiar with the arithmetic of numerical fractions

#### Learning Outcomes

- add, subtract, multiply and divide algebraic fractions

#### Contents

1 Cancelling common factors2 Multiplication and division of algebraic fractions

3 Addition and subtraction of algebraic fractions