Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
x2+6x33x27x+12+2=x28x9x27x+12.\frac{ - x^2 + 6 x - 33 }{ x^2 - 7 x + 12 } + 2=\frac{ x^2 - 8 x - 9 }{ x^2 - 7 x + 12 }.
Hence, without using a calculator, solve the inequality
x2+6x33x27x+12<2\frac{ - x^2 + 6 x - 33 }{ x^2 - 7 x + 12 } < -2
[5]

Answer