Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
x2+12x+21x22x3+2=x2+8x+15x22x3.\frac{ - x^2 + 12 x + 21 }{ x^2 - 2 x - 3 } + 2=\frac{ x^2 + 8 x + 15 }{ x^2 - 2 x - 3 }.
Hence, without using a calculator, solve the inequality
x2+12x+21x22x3>2\frac{ - x^2 + 12 x + 21 }{ x^2 - 2 x - 3 } > -2
[5]

Answer