June 2017 Paper 1 Q11
11 Simplify fully \(\qquad \dfrac{x}{x - 3} + \dfrac{6}{(x - 3)(x - 5)}\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| common denominator \((x - 3)(x - 5)\) oe | M1 | allow \((x - 3)^2(x - 5)\) oe |
| numerator \(x(x - 5) + 6\) or \(x^2 - 5x + 6\) | M1dep | allow \(x(x - 3)(x - 5) + 6(x - 3)\) oe |
| \(\dfrac{(x - 3)(x - 2)}{(x - 3)(x - 5)}\) | A1 | \(\dfrac{(x - 3)^2(x - 2)}{(x - 3)^2(x - 5)}\) |
| \(\dfrac{x - 2}{x - 5}\) | A1 | |
| Alternative method 2 | ||
| \(\dfrac{1}{(x - 3)}\left(x + \dfrac{6}{(x - 5)}\right)\) | M1 | |
| \(\dfrac{1}{(x - 3)}\left(\dfrac{x(x - 5) + 6}{(x - 5)}\right)\) or \(\dfrac{1}{(x - 3)}\left(\dfrac{x^2 - 5x + 6}{(x - 5)}\right)\) | M1 | |
| \(\dfrac{(x - 3)(x - 2)}{(x - 3)(x - 5)}\) | A1 | |
| \(\dfrac{x - 2}{x - 5}\) | A1 | |
Additional guidance
Further work eg answer of \(\dfrac{-2}{-5}\) means the final A1 must not be awarded
eg \(\dfrac{x(x - 5)}{(x - 3)(x - 5)} + \dfrac{6}{(x - 3)(x - 5)}\) scores M1 M1
Either ... follow the LHS of the mark scheme for the first three steps
Or ... follow the RHS
... do not mix expressions ... the numerators and denominators must match