Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
12x+27x2+2x3+1=x210x+24x2+2x3.\frac{ - 12 x + 27 }{ x^2 + 2 x - 3 } + 1=\frac{ x^2 - 10 x + 24 }{ x^2 + 2 x - 3 }.
Hence, without using a calculator, solve the inequality
12x+27x2+2x3>1\frac{ - 12 x + 27 }{ x^2 + 2 x - 3 } > -1
[5]

Answer