1MA0 Higher June 2016 Paper 2 Q24

(a) Simplify fully \[\frac{3 - x}{3x^2 - 5x - 12}\] (2)

(b) Write \[\frac{x}{x - 1} - \frac{x}{x + 1}\] as a single fraction in its simplest form. (3)

Answer	Mark	Notes
\(\dfrac{-1}{3x + 4}\)	2	M1 for \((3x \pm 4)(x \pm 3)\) or \((-3x \pm 4)(-x \pm 3)\) A1 for \(\dfrac{-1}{3x + 4}\), accept \(\dfrac{1}{-3x - 4}\)

Mark scheme (b)

Answer	Mark	Notes
\(\dfrac{2x}{x^2 - 1}\)	3	M1 for common denominator \((x - 1)(x + 1)\) or \(x^2 - 1\) M1 for \(\dfrac{x(x + 1)}{(x - 1)(x + 1)} - \dfrac{x(x - 1)}{(x - 1)(x + 1)}\) oe or \(\dfrac{x(x + 1) - x(x - 1)}{(x - 1)(x + 1)}\) oe (NB: The denominator must be \((x - 1)(x + 1)\) or \(x^2 - 1\) or another suitable common denominator) A1 for \(\dfrac{2x}{(x - 1)(x + 1)}\) or \(\dfrac{2x}{x^2 - 1}\)