Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
3x26x+75x2+5x+62=x216x+63x2+5x+6.\frac{ 3 x^2 - 6 x + 75 }{ x^2 + 5 x + 6 } - 2=\frac{ x^2 - 16 x + 63 }{ x^2 + 5 x + 6 }.
Hence, without using a calculator, solve the inequality
3x26x+75x2+5x+6>2\frac{ 3 x^2 - 6 x + 75 }{ x^2 + 5 x + 6 } > 2
[5]

Answer