Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
4x233x+59x29x+183=x26x+5x29x+18.\frac{ 4 x^2 - 33 x + 59 }{ x^2 - 9 x + 18 } - 3=\frac{ x^2 - 6 x + 5 }{ x^2 - 9 x + 18 }.
Hence, without using a calculator, solve the inequality
4x233x+59x29x+18<3\frac{ 4 x^2 - 33 x + 59 }{ x^2 - 9 x + 18 } < 3
[5]

Answer