Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
x22x+21x22x8+2=x26x+5x22x8.\frac{ - x^2 - 2 x + 21 }{ x^2 - 2 x - 8 } + 2=\frac{ x^2 - 6 x + 5 }{ x^2 - 2 x - 8 }.
Hence, without using a calculator, solve the inequality
x22x+21x22x8>2\frac{ - x^2 - 2 x + 21 }{ x^2 - 2 x - 8 } > -2
[5]

Answer