Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x24x55x26x+81=x2+2x63x26x+8.\frac{ 2 x^2 - 4 x - 55 }{ x^2 - 6 x + 8 } - 1=\frac{ x^2 + 2 x - 63 }{ x^2 - 6 x + 8 }.
Hence, without using a calculator, solve the inequality
2x24x55x26x+8<1\frac{ 2 x^2 - 4 x - 55 }{ x^2 - 6 x + 8 } < 1
[5]

Answer