Higher June 2017 Paper 2 Q19
19 \(2 - \dfrac{x + 2}{x - 3} - \dfrac{x - 6}{x + 3}\) can be written as a single fraction in the form \(\dfrac{ax + b}{x^2 - 9}\) where \(a\) and \(b\) are integers.
Work out the value of \(a\) and the value of \(b\). (4)
| Answer | Mark | Notes |
|---|---|---|
| \(a = 4\), \(b = -42\) | M1 | for at least two terms from \(2(x - 3)(x + 3)\), \((x + 2)(x + 3)\), \((x - 6)(x - 3)\) |
| M1 | (dep) for the correct expansion of at least two expressions, irrespective of signs, eg. \(2x^2 - 18\), \(x^2 + 2x + 3x + 6\), \(x^2 - 6x - 3x + 18\) oe | |
| M1 | for \(2x^2 - 18 - x^2 - 5x - 6 - x^2 + 9x - 18\) | |
| A1 | for \(a = 4\), \(b = -42\) (accept \(4x - 42\)) |