Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+8x+54x2+x12+3=x2+11x+18x2+x12.\frac{ - 2 x^2 + 8 x + 54 }{ x^2 + x - 12 } + 3=\frac{ x^2 + 11 x + 18 }{ x^2 + x - 12 }.
Hence, without using a calculator, solve the inequality
2x2+8x+54x2+x12<3\frac{ - 2 x^2 + 8 x + 54 }{ x^2 + x - 12 } < -3
[5]

Answer