Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
3x2+10x+23x2x22=x2+12x+27x2x2.\frac{ 3 x^2 + 10 x + 23 }{ x^2 - x - 2 } - 2=\frac{ x^2 + 12 x + 27 }{ x^2 - x - 2 }.
Hence, without using a calculator, solve the inequality
3x2+10x+23x2x2<2\frac{ 3 x^2 + 10 x + 23 }{ x^2 - x - 2 } < 2
[5]

Answer