Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
4x2+34x+57x2+8x+123=x2+10x+21x2+8x+12.\frac{ 4 x^2 + 34 x + 57 }{ x^2 + 8 x + 12 } - 3=\frac{ x^2 + 10 x + 21 }{ x^2 + 8 x + 12 }.
Hence, without using a calculator, solve the inequality
4x2+34x+57x2+8x+12<3\frac{ 4 x^2 + 34 x + 57 }{ x^2 + 8 x + 12 } < 3
[5]

Answer