## Simplifying Fractions Involving Algebraic Expressions

Some questions will ask you to simplify a fraction which has pronumerals in it to its simplest form.  Sometimes this will be quite easy, such as for this fraction:

The 8 on 4 simplifies to 2 on 1, and the ‘q squared on q’ part simplifies to just ‘q on 1’:

There are much more complicated fractions though which require a bit more thought and fiddling around before you can simplify them.  There are a few things you can look for to help you simplify the fraction:

-     Look for common factors that you can divide the top and bottom of the equation by.  In the last fraction, ‘4’ and ‘q’ were common factors.

-     See if any parts of the top or bottom are perfect squares – if they are you can factorise them.

-     See if any parts of the top or bottom are in the ‘difference of two squares’ format – if so you will be able to factorise them.

-     See if you can factorise the tops or bottoms in any other way.

Here’s how to use these for a more complicated fraction: