Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
x2+20x+84x23x18+2=x2+14x+48x23x18.\frac{ - x^2 + 20 x + 84 }{ x^2 - 3 x - 18 } + 2=\frac{ x^2 + 14 x + 48 }{ x^2 - 3 x - 18 }.
Hence, without using a calculator, solve the inequality
x2+20x+84x23x18>2\frac{ - x^2 + 20 x + 84 }{ x^2 - 3 x - 18 } > -2
[5]

Answer