Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
x2+11x46x26x+8+2=x2x30x26x+8.\frac{ - x^2 + 11 x - 46 }{ x^2 - 6 x + 8 } + 2=\frac{ x^2 - x - 30 }{ x^2 - 6 x + 8 }.
Hence, without using a calculator, solve the inequality
x2+11x46x26x+8>2\frac{ - x^2 + 11 x - 46 }{ x^2 - 6 x + 8 } > -2
[5]

Answer