Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
3x2+18x+39x2+10x+212=x22x3x2+10x+21.\frac{ 3 x^2 + 18 x + 39 }{ x^2 + 10 x + 21 } - 2=\frac{ x^2 - 2 x - 3 }{ x^2 + 10 x + 21 }.
Hence, without using a calculator, solve the inequality
3x2+18x+39x2+10x+21<2\frac{ 3 x^2 + 18 x + 39 }{ x^2 + 10 x + 21 } < 2
[5]

Answer