Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+6x+9x2+8x+121=x22x3x2+8x+12.\frac{ 2 x^2 + 6 x + 9 }{ x^2 + 8 x + 12 } - 1=\frac{ x^2 - 2 x - 3 }{ x^2 + 8 x + 12 }.
Hence, without using a calculator, solve the inequality
2x2+6x+9x2+8x+12>1\frac{ 2 x^2 + 6 x + 9 }{ x^2 + 8 x + 12 } > 1
[5]

Answer