Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+3x18x2+4x121=x2x6x2+4x12.\frac{ 2 x^2 + 3 x - 18 }{ x^2 + 4 x - 12 } - 1=\frac{ x^2 - x - 6 }{ x^2 + 4 x - 12 }.
Hence, without using a calculator, solve the inequality
2x2+3x18x2+4x12<1\frac{ 2 x^2 + 3 x - 18 }{ x^2 + 4 x - 12 } < 1
[5]

Answer