Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+12x19x26x+8+3=x26x+5x26x+8.\frac{ - 2 x^2 + 12 x - 19 }{ x^2 - 6 x + 8 } + 3=\frac{ x^2 - 6 x + 5 }{ x^2 - 6 x + 8 }.
Hence, without using a calculator, solve the inequality
2x2+12x19x26x+8<3\frac{ - 2 x^2 + 12 x - 19 }{ x^2 - 6 x + 8 } < -3
[5]

Answer