1. Simplifying Algebraic Fractions

2. When x and y are positive integers,
Law of indices
When x and y are positive integers,
1. ax × ay = ax+y
2. ax ÷ ay = ax-y

3. Start with Algebraic Fraction Write out the expression in parts
Simplifying Powers
20xcxcxcxdxdxdxd
4xcxcxd
20c3d4
4c2d
Start with Algebraic Fraction
Write out the expression in parts
Cancel the like terms
Rewrite the fraction
Cancel the numbers
Final answer
20cd3 4
If you are confident, use the rule to get to the answer quicker: ax ÷ ay = ax-y 5 1 d4 d1
5cd3
e.g.
= d4-1
= d3

4. Simplifying by Factorising 1
Start with Algebraic Fraction
Factorise the Numerator
Cancel the numbers
Final answer
5t+15
5t2
5(t+3)
5t2
5(t+3)
5t2
t+3 t2

5. Simplifying by Factorising 2 Start with Algebraic Fraction
Factorise the Numerator
Cancel the like terms
Cancel the numbers
Final answer
3rs+6r2 9r
3r(s+2r) 9r
3r(s+2r) 9r 1
3(s+2r) 9 3
s+2r 3

6. Simplifying with Quadratics
Start with Algebraic Fraction
Factorise both quadratics
Cancel the brackets
Final answer
2x2+x-3
x2-1
(2x+3)(x-1)
(x+1)(x-1)
(2x+3)(x-1)
(x+1)(x-1)
2x+3
x+1

7. Questions Simplify 18b3c4 9bc3 36u+4 4u2 4mn+6m3 8m x2+7x+12 x2+10x+21

8. Simplifying Algebraic Fractions by K Islania (2017) of English Martyrs’ Catholic School. This work is licensed under a Creative Commons Attribution 4.0 International License.