Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
x223x+84x2+6x27+2=x211x+30x2+6x27.\frac{ - x^2 - 23 x + 84 }{ x^2 + 6 x - 27 } + 2=\frac{ x^2 - 11 x + 30 }{ x^2 + 6 x - 27 }.
Hence, without using a calculator, solve the inequality
x223x+84x2+6x27<2\frac{ - x^2 - 23 x + 84 }{ x^2 + 6 x - 27 } < -2
[5]

Answer