Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x28x30x27x+121=x2x42x27x+12.\frac{ 2 x^2 - 8 x - 30 }{ x^2 - 7 x + 12 } - 1=\frac{ x^2 - x - 42 }{ x^2 - 7 x + 12 }.
Hence, without using a calculator, solve the inequality
2x28x30x27x+12>1\frac{ 2 x^2 - 8 x - 30 }{ x^2 - 7 x + 12 } > 1
[5]

Answer