# Simplify by Cancelling Common Factors

## Simplifying Algebraic Fractions With Powers by Cancelling Common Factors

Here is a simple algebraic fraction. We will now try to simplify it by cancelling
common factors. The first thing we ´should do is rewrite the fraction writing it out
in parts (a²= a x a). Then we can cancel common factors. We have removed one
b and 2 a from the top and the bottom. Then we were also able to simplify 9 and
3 since they are both factors of 9. We ended up with 3ab over 1. Since we have a 1 as a denominator we can just ignore the 1 and write the fraction as a
normal number. All simple algebraic fractions with powers can be solved using this method

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Example 1
We have simplified this fraction by factorising it. This allowed us to cancel some of the common factors. At the end, we were able to
solve the algebraic fraction using simple fractional multiplication skills.

Example 2
We could not simplify this fraction as much as the previous one as there were not a lot of common factors. However, we were able to
simplify the fraction enough in order for us to be able to solve it easily.

## Simplifying Algebraic Fractions using Factorisation

The more common method which we use to simplify algebraic
fractions is to factorise the fractions using brackets. We have to
do this since we cannot just cancel numbers or letters out of
algebraic expressions. In the example on the right, we have simplified the algebraic fraction by factorising it. We have factorised the numerator and the
denominator of first fraction. We were then able to cancel (x-3) four times. Which allowed us to reduce the fraction so that it only had numbers
remaining. We were then able to simplify the fraction and even solve it. It does not happen very often that you can cancel all the unknown.

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Chapter 19.1: Learning Outcomes
Students will learn how to simplify algebraic fractions by cancelling
common factors!
Students will learn how to simplify algebraic fractions using factorisation!

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