Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+15x+62x23x18+3=x2+6x+8x23x18.\frac{ - 2 x^2 + 15 x + 62 }{ x^2 - 3 x - 18 } + 3=\frac{ x^2 + 6 x + 8 }{ x^2 - 3 x - 18 }.
Hence, without using a calculator, solve the inequality
2x2+15x+62x23x18<3\frac{ - 2 x^2 + 15 x + 62 }{ x^2 - 3 x - 18 } < -3
[5]

Answer