Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
3x213x18x27x+62=x2+x30x27x+6.\frac{ 3 x^2 - 13 x - 18 }{ x^2 - 7 x + 6 } - 2=\frac{ x^2 + x - 30 }{ x^2 - 7 x + 6 }.
Hence, without using a calculator, solve the inequality
3x213x18x27x+6<2\frac{ 3 x^2 - 13 x - 18 }{ x^2 - 7 x + 6 } < 2
[5]

Answer