Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
3x2+19x+14x2+9x+82=x2+x2x2+9x+8.\frac{ 3 x^2 + 19 x + 14 }{ x^2 + 9 x + 8 } - 2=\frac{ x^2 + x - 2 }{ x^2 + 9 x + 8 }.
Hence, without using a calculator, solve the inequality
3x2+19x+14x2+9x+8<2\frac{ 3 x^2 + 19 x + 14 }{ x^2 + 9 x + 8 } < 2
[5]

Answer