Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x26x+62x2+5x14+3=x2+9x+20x2+5x14.\frac{ - 2 x^2 - 6 x + 62 }{ x^2 + 5 x - 14 } + 3=\frac{ x^2 + 9 x + 20 }{ x^2 + 5 x - 14 }.
Hence, without using a calculator, solve the inequality
2x26x+62x2+5x14<3\frac{ - 2 x^2 - 6 x + 62 }{ x^2 + 5 x - 14 } < -3
[5]

Answer