Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
x25x26x2+5x+6+2=x2+5x14x2+5x+6.\frac{ - x^2 - 5 x - 26 }{ x^2 + 5 x + 6 } + 2=\frac{ x^2 + 5 x - 14 }{ x^2 + 5 x + 6 }.
Hence, without using a calculator, solve the inequality
x25x26x2+5x+6>2\frac{ - x^2 - 5 x - 26 }{ x^2 + 5 x + 6 } > -2
[5]

Answer