Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+18x+68x24x21+3=x2+6x+5x24x21.\frac{ - 2 x^2 + 18 x + 68 }{ x^2 - 4 x - 21 } + 3=\frac{ x^2 + 6 x + 5 }{ x^2 - 4 x - 21 }.
Hence, without using a calculator, solve the inequality
2x2+18x+68x24x21<3\frac{ - 2 x^2 + 18 x + 68 }{ x^2 - 4 x - 21 } < -3
[5]

Answer