Higher November 2018 Paper 6 Q21
21 Show that \(\dfrac{5x}{x + 5} + \dfrac{25}{x - 7} - \dfrac{300}{(x + 5)(x - 7)}\) simplifies to an integer. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 5 nfww and after \(\dfrac{5(x + 5)(x - 7)}{(x + 5)(x - 7)}\) seen | 6 | B1 for \((x + 5)(x - 7)\) or \(x^2 + 5x - 7x - 35\) or better seen as a common denominator of the first two fractions AND B3 for numerator \(5x^2 - 10x - 175\) or B2 for numerator \(5x^2 - 10x + 125\) or M1 for \(5x(x - 7)\) and \(25(x + 5)\) AND M1 for \(5(x^2 - 2x - 35)\) or \((5x + 25)(x - 7)\) or \((x + 5)(5x - 35)\) or \(5(x + 5)(x - 7)\) | Condone missing final bracket. Condone numerators written without any denominators or with an incorrect common denominator |