Introduction

An algebraic fraction is a fraction that contains algebraic terms. To manipulate algebraic fractions, treat them like numerical fractions, i.e. the same rules associated with numerical fractions are applicable. The value of the fraction remains the same if we multiply or divide both the numerator and denominator by the same non-zero expression.

To simplify algebraic fractions, we divide the numerator and denominator by their common factors, i.e. cancelling common factors. 

Watch the following video for an example of how this is done:

Multiplication of Algebraic Fractions

Algebraic fractions are multiplied the same way as numeric fractions. To do so,
1. Divide the numerator and denominator by the common factors, i.e. cancelling common factors. 
2. Multiply the terms that are left in the numerator and multiply the terms that are left in the denominator.

Watch the following video for a worked example: 

Division of Algebraic Fractions

Algebraic fractions are divided the same way as numeric fractions. To divide a fraction is the same as multiplying by its reciprocal. 

To divide two algebraic fractions,
Multiply the first fraction by the reciprocal of the second fraction. 
For example, a ÷ b = a x 1/b = a/b

Watch the following video for a worked example:

LCM Worked Example

We have learnt previously how to find the HCF and LCM of integers. In this chapter, you will learn to find the HCF and LCM of algebraic expressions. 

Watch the following worked example for how LCM can be found:

LCM Video Example

The following video is a worked example of how LCM of algebraic expressions can be found:

HCM Worked example

Here is a worked example of how HCF of algebraic expressions can be found:

Video Explanation

Algebraic fractions are added and subtracted in the same way as numeric fractions. To do so:
1. Find the LCM of the denominators first.
2. Write the algebraic fractions as equivalent fractions with the same denominators. 
3. Add or subtract as we do in numeric fractions.

The following video is shows in greater detail how this is done:

Explanation

To solve equations involving algebraic fractions,

1. Eliminate the denominators by multiplying each term of the equation by the LCM of the denominators.
2. Solve the new equivalent equation.

Worked Example 1

View the following:

Worked Example 2