Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
3x2+14x+4x2+9x+182=x24x32x2+9x+18.\frac{ 3 x^2 + 14 x + 4 }{ x^2 + 9 x + 18 } - 2=\frac{ x^2 - 4 x - 32 }{ x^2 + 9 x + 18 }.
Hence, without using a calculator, solve the inequality
3x2+14x+4x2+9x+18<2\frac{ 3 x^2 + 14 x + 4 }{ x^2 + 9 x + 18 } < 2
[5]

Answer