Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x218x+12x27x181=x211x+30x27x18.\frac{ 2 x^2 - 18 x + 12 }{ x^2 - 7 x - 18 } - 1=\frac{ x^2 - 11 x + 30 }{ x^2 - 7 x - 18 }.
Hence, without using a calculator, solve the inequality
2x218x+12x27x18<1\frac{ 2 x^2 - 18 x + 12 }{ x^2 - 7 x - 18 } < 1
[5]

Answer