Higher June 2023 Paper 2 Q14
14 Show that \(\dfrac{x^2 - x - 6}{2x^2 - 5x - 3}\) can be written in the form \(\dfrac{ax + b}{cx + d}\) where \(a\), \(b\), \(c\) and \(d\) are integers. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{x + 2}{2x + 1}\) | M1 | for correctly factorising one expression, eg \((x - 3)(x + 2)\) or \((x - 3)(2x + 1)\) |
| M1 | for factorising both expressions, eg \((x - 3)(x + 2)\) and \((x - 3)(2x + 1)\) | |
| A1 | oe or \(a = 1\), \(b = 2\), \(c = 2\), \(d = 1\) |
Additional guidance
eg \(\dfrac{2 + x}{1 + 2x}\), \(\dfrac{-x - 2}{-2x - 1}\)