Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+14x+26x2+3x41=x2+11x+30x2+3x4.\frac{ 2 x^2 + 14 x + 26 }{ x^2 + 3 x - 4 } - 1=\frac{ x^2 + 11 x + 30 }{ x^2 + 3 x - 4 }.
Hence, without using a calculator, solve the inequality
2x2+14x+26x2+3x4>1\frac{ 2 x^2 + 14 x + 26 }{ x^2 + 3 x - 4 } > 1
[5]

Answer