Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
7x47x2+8x9+1=x2+x56x2+8x9.\frac{ - 7 x - 47 }{ x^2 + 8 x - 9 } + 1=\frac{ x^2 + x - 56 }{ x^2 + 8 x - 9 }.
Hence, without using a calculator, solve the inequality
7x47x2+8x9<1\frac{ - 7 x - 47 }{ x^2 + 8 x - 9 } < -1
[5]

Answer