Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+8x54x24x+3+3=x24x45x24x+3.\frac{ - 2 x^2 + 8 x - 54 }{ x^2 - 4 x + 3 } + 3=\frac{ x^2 - 4 x - 45 }{ x^2 - 4 x + 3 }.
Hence, without using a calculator, solve the inequality
2x2+8x54x24x+3>3\frac{ - 2 x^2 + 8 x - 54 }{ x^2 - 4 x + 3 } > -3
[5]

Answer