Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+18x96x26x+5+3=x281x26x+5.\frac{ - 2 x^2 + 18 x - 96 }{ x^2 - 6 x + 5 } + 3=\frac{ x^2 - 81 }{ x^2 - 6 x + 5 }.
Hence, without using a calculator, solve the inequality
2x2+18x96x26x+5>3\frac{ - 2 x^2 + 18 x - 96 }{ x^2 - 6 x + 5 } > -3
[5]

Answer