Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+25x+71x2+9x+81=x2+16x+63x2+9x+8.\frac{ 2 x^2 + 25 x + 71 }{ x^2 + 9 x + 8 } - 1=\frac{ x^2 + 16 x + 63 }{ x^2 + 9 x + 8 }.
Hence, without using a calculator, solve the inequality
2x2+25x+71x2+9x+8<1\frac{ 2 x^2 + 25 x + 71 }{ x^2 + 9 x + 8 } < 1
[5]

Answer