Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
3x2+21x+4x2+6x72=x2+9x+18x2+6x7.\frac{ 3 x^2 + 21 x + 4 }{ x^2 + 6 x - 7 } - 2=\frac{ x^2 + 9 x + 18 }{ x^2 + 6 x - 7 }.
Hence, without using a calculator, solve the inequality
3x2+21x+4x2+6x7>2\frac{ 3 x^2 + 21 x + 4 }{ x^2 + 6 x - 7 } > 2
[5]

Answer