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

Examples 1 1 3 1 1 1 1 1

Remember: only complete brackets can be cancelled 1 1 1 1 Remember: only complete brackets can be cancelled

1 1 1 4 1 1

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)

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)

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

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)

Simplify

Simplify

4

3

Solve

Solve

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