Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x34x2+x6+1=x2+3x40x2+x6.\frac{ 2 x - 34 }{ x^2 + x - 6 } + 1=\frac{ x^2 + 3 x - 40 }{ x^2 + x - 6 }.
Hence, without using a calculator, solve the inequality
2x34x2+x6<1\frac{ 2 x - 34 }{ x^2 + x - 6 } < -1
[5]

Answer