1. Fraction in Simplest form
We can sometimes reduce fractions to a simpler form if the numerator and denominator have a number or letter in common.
Examples
HCF = y
HCF = 3

2. Examples 1 1 3 1 1 1 1 1

3. Remember: only complete brackets can be cancelled1 1 1 1
Remember: only complete brackets can be cancelled

4. 1 1 1 4 1 1

5. Factorise numerator and denominator
x2 + 7x + 12
Find factors of 12 that add to 7
= (x + 3)(x + 4)
x2 – 9
Difference of two squares
= (x + 3)(x – 3)

6. Factorise numerator and denominator
x2 + x – 6
Find factors of –6 that add to +1
= (x + 3)(x – 2)
x2 – 7x + 10
Find factors of 10 that add to –7
= (x – 5)(x – 2)

7. Adding Algebraic Fractions
Kiss and smile ( )
3(x + 1) + x 18 + 5 = =
x(x + 1) 30
3x x = 23 =
x(x + 1) 30
4x + 3 =
x(x + 1)

8. Subtracting Algebraic Fractions
Kiss and smile ( )
5(a – 3) 2a – 20 – 7 = =
a(a – 3) 35
5a – 15 – 2a = 13 =
a(a – 3) 35
3a – 15 =
a(a – 3)

9. Simplify

10. Simplify

12. 4

14. 3

16. Solve

17. Solve

18. Multiply out those brackets – watch out for those negative signs!
x + 3 4
x+3 4 - -
= 6 
= 6
x² – 9
x + 1
(x+3)(x-3)
x+1
LET’S FACTORISE! 1 4 -
= 6
Multiply out those brackets
– watch out for those negative signs!
(x-3)
x+1
(x+1) - 4(x-3)
= 6
(x-3)(x+1)
(x+1) – 4(x-3)
= 6
(x-3) (x+1)
x + 1 – 4x +12 = 6(x² – 3x + x – 3)
Solution is
x = - 1∙64 or 3∙14
Quadratic to solve is
0 = 6x² – 9x – 31