# Simplifying rational expressions

Simplifying expressions or algebraic fractions works in the same way as simplifying normal fractions. A common must be found and divided throughout. For example, to simplify the fraction , look for a common factor between 12 and 16. This is 4 as and .

Divide 4 throughout the fraction, which gives .

### Example 1

Simplify .

To simplify this, look for the of and . This is . Take this common factor out of each part of the fraction.

This gives .

This fraction cannot be simplified any further so this is the final answer.

Question

Simplify .

The highest common factor of and is . Divide this common factor through the and .

This gives .

This fraction cannot be simplified any further so this is the final answer.

Question

Simplify .

The highest common factor of and is . Dividing this throughout the fraction gives .

There are no more common factors in this fraction, so this is the final answer.