Higher November 2019 Paper 4 Q16
16 Show that \(\dfrac{x + 9}{x^2 - 1} + \dfrac{4}{x + 1}\) can be written in the form \(\dfrac{a}{x - 1}\), where \(a\) is an integer. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{4(x - 1)}{x^2 - 1}\) oe | M1 | also allow method with denominator \((x^2 - 1)(x + 1)\) e.g. | |
| \(x + 9 + 4x - 4\) or \(5x + 5\) | M1 | M1 for \(\frac{(x + 9)(x + 1)}{(x^2 - 1)(x + 1)}\) or \(\frac{4(x^2 - 1)}{(x^2 - 1)(x + 1)}\) M1 for \(x^2 + 9x + x + 9 + 4x^2 - 4\) or better | |
| numerator = \(5(x + 1)\) | A1 | ||
| denominator = \((x + 1)(x - 1)\) | A1 | If 0 scored SC1 for \(x^2 - 1 = (x + 1)(x - 1)\) | |