Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
4x28x3x24x+33=x2+4x12x24x+3.\frac{ 4 x^2 - 8 x - 3 }{ x^2 - 4 x + 3 } - 3=\frac{ x^2 + 4 x - 12 }{ x^2 - 4 x + 3 }.
Hence, without using a calculator, solve the inequality
4x28x3x24x+3<3\frac{ 4 x^2 - 8 x - 3 }{ x^2 - 4 x + 3 } < 3
[5]

Answer