Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x27x31x25x+41=x22x35x25x+4.\frac{ 2 x^2 - 7 x - 31 }{ x^2 - 5 x + 4 } - 1=\frac{ x^2 - 2 x - 35 }{ x^2 - 5 x + 4 }.
Hence, without using a calculator, solve the inequality
2x27x31x25x+4>1\frac{ 2 x^2 - 7 x - 31 }{ x^2 - 5 x + 4 } > 1
[5]

Answer