Year 9 Interactive Maths - Second Edition

Rational Expressions

Recall that:

An expression that is written in the form of a fraction (or ratio) is called a rational expression.

Simplification of Rational Expressions

In general:

From this, we can say that:

Only factors can be cancelled.

This suggests that the division by 3 is not permissible.  In other words, we can not cancel 3 as it is not a factor of the numerator.

Example 1

Solution:

Often, we set out the solution as follows:

Example 2

Solution:

We often use the following steps to simplify algebraic fractions:

• Factorise the numerator and denominator.
• Cancel the factors that are common to the numerator and denominator.

This process is called reducing the fraction to its lowest terms.

Example 3

Solution:

Example 4

Solution:

Remember:

Factorise and then cancel the common factors.

Example 5

Solution:

Example 6

Solution:

Key Terms

rational expression