4400 Higher November 2010 Paper 4 Q22

22 Simplify fully \(1 + \dfrac{x^2 + x - 6}{(x + 4)(x - 2)}\)

(4)

Mark scheme

Scheme	Marks
\(1 + \dfrac{(x + 3)(x - 2)}{(x + 4)(x - 2)}\) or \(\dfrac{(x + 4)(x - 2) + x^2 + x - 6}{(x + 4)(x - 2)}\) or \(\dfrac{(x + 4)(x - 2) + x^2 + x - 6}{x^2 + 2x - 8}\)	B1
\(1 + \dfrac{x + 3}{x + 4}\) or \(\dfrac{2x^2 + 3x - 14}{(x + 4)(x - 2)}\) or \(\dfrac{2x^2 + 3x - 14}{x^2 + 2x - 8}\) or \(\dfrac{(x - 2)[(x + 4) + (x + 3)]}{(x + 4)(x - 2)}\)	B1
\(\dfrac{x + 4 + x + 3}{x + 4}\) or \(\dfrac{x + 4}{x + 4} + \dfrac{x + 3}{x + 4}\) or \(\dfrac{(2x + 7)(x - 2)}{(x + 4)(x - 2)}\)	B1
\(\dfrac{2x + 7}{x + 4}\)	B1
	(4)
	(4 marks)

B1: for correct factorisation or for correct single fraction, even if unsimplified