Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
4x2+38x+82x2+9x+183=x2+11x+28x2+9x+18.\frac{ 4 x^2 + 38 x + 82 }{ x^2 + 9 x + 18 } - 3=\frac{ x^2 + 11 x + 28 }{ x^2 + 9 x + 18 }.
Hence, without using a calculator, solve the inequality
4x2+38x+82x2+9x+18<3\frac{ 4 x^2 + 38 x + 82 }{ x^2 + 9 x + 18 } < 3
[5]

Answer