Higher November 2020 Paper 6 Q21
21 Write as a single fraction in its simplest form.
\[\frac{x}{x + 2} + \frac{x + 1}{x - 2} - \frac{6x}{x^2 - 4}\] [6]| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{2x - 1}{x + 2}\) as final answer | 6 | M1 for \(x^2 - 4 = (x + 2)(x - 2)\) soi in the denominator AND M3 for all 3 fractions combined with quadratic common denominator and expanded numerator or M2 for correct products on numerator of at least 2 equivalent fractions that are consistent with their common denominators or M1 for correct product on numerator of 1 fraction that is consistent with an attempted common denominator AND M1dep for \(\frac{(2x - 1)(x - 2)}{(x + 2)(x - 2)}\) or \(\frac{(2x - 1)(x - 2)}{x^2 - 4}\) (dep on previous M3 earned) | e.g. \(\frac{6x}{(x + 2)(x - 2)}\) seen, or a common denominator of \((x + 2)(x - 2)\) later expanded to \(x^2 - 4\) e.g. \(\frac{x^2 - 2x + x^2 + x + 2x + 2 - 6x}{(x + 2)(x - 2)}\) soi by \(\frac{2x^2 - 5x + 2}{(x + 2)(x - 2)}\) e.g. \(\frac{x(x - 2)}{(x + 2)(x - 2)}\) oe and \(\frac{(x + 1)(x + 2)}{(x + 2)(x - 2)}\) oe e.g. \(\frac{x(x - 2)}{(x + 2)(x - 2)}\) oe Factorises numerator of combined fraction Can earn up to M1 + M2 + M0 for common denominator used that is not in its lowest terms. eg. M0 + M2 for \(\frac{x(x - 2)(x^2 - 4)}{(x + 2)(x - 2)(x^2 - 4)}\) and \(\frac{(x + 1)(x + 2)(x^2 - 4)}{(x + 2)(x - 2)(x^2 - 4)}\) eg. M1 + M1 for \(\frac{x(x - 2)(x + 2)(x - 2)}{(x + 2)(x - 2)(x + 2)(x - 2)}\) |