Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x211x+75x2+7x18+3=x2+10x+21x2+7x18.\frac{ - 2 x^2 - 11 x + 75 }{ x^2 + 7 x - 18 } + 3=\frac{ x^2 + 10 x + 21 }{ x^2 + 7 x - 18 }.
Hence, without using a calculator, solve the inequality
2x211x+75x2+7x18<3\frac{ - 2 x^2 - 11 x + 75 }{ x^2 + 7 x - 18 } < -3
[5]

Answer