Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+5x+53x29x+81=x2+14x+45x29x+8.\frac{ 2 x^2 + 5 x + 53 }{ x^2 - 9 x + 8 } - 1=\frac{ x^2 + 14 x + 45 }{ x^2 - 9 x + 8 }.
Hence, without using a calculator, solve the inequality
2x2+5x+53x29x+8>1\frac{ 2 x^2 + 5 x + 53 }{ x^2 - 9 x + 8 } > 1
[5]

Answer