Higher November 2019 Paper 3 Q22
22 Show that \(\dfrac{7x - 14}{x^2 + 4x - 12} \div \dfrac{x - 6}{x^3 - 36x}\) simplifies to \(ax\) where \(a\) is an integer. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(7x\) | M1 | multiplication by reciprocal, eg \(\dfrac{7(x - 2)}{(x - 2)(x + 6)} \times \dfrac{x(x + 6)(x - 6)}{x - 6}\) |
| M1 | for factorising the numerator or denominator of the 1st fraction, eg \(\dfrac{7(x - 2)}{(x - 2)(x + 6)}\) or \(\dfrac{7(x - 2)}{x^2 + 4x - 12}\) or \(\dfrac{7x - 14}{(x - 2)(x + 6)}\) | |
| M1 | for factorising the denominator of the second fraction, eg \(\dfrac{x - 6}{x(x + 6)(x - 6)}\ \left(= \dfrac{1}{x(x + 6)}\right)\) | |
| A1 | completing the algebra to reach \(7x\) |
Additional guidance
Independent mark, may be awarded at any point