Higher June 2018 Paper 2R Q22
22 Express \(\dfrac{4x^2 - 25}{5x^2 + 2x - 7} \times \left(\dfrac{2}{x - 3} - \dfrac{3}{2x - 5}\right)\) as a single fraction in its simplest form.
(4)
| Scheme | Marks |
|---|---|
| \(\dfrac{(2x + 5)(2x - 5)}{(5x + 7)(x - 1)} \times \dfrac{2(2x - 5) - 3(x - 3)}{(x - 3)(2x - 5)}\) | M1 |
| M1 | |
| \(\dfrac{(2x + 5)(2x - 5)}{(5x + 7)(x - 1)} \times \dfrac{x - 1}{(x - 3)(2x - 5)}\) | M1 |
| \(\dfrac{2x + 5}{(5x + 7)(x - 3)}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: For \(4x^2 - 25 = (2x + 5)(2x - 5)\) or \(5x^2 + 2x - 7 = (5x + 7)(x - 1)\)
M1: \(\dfrac{2}{x - 3} - \dfrac{3}{2x - 5} = \dfrac{2(2x - 5) - 3(x - 3)}{(x - 3)(2x - 5)}\) oe
M1: \(\dfrac{(2x + 5)(2x - 5)}{(5x + 7)(x - 1)} \times \dfrac{x - 1}{(x - 3)(2x - 5)}\) oe, may be partially simplified
A1: Denominator may be expanded eg \(\dfrac{2x + 5}{5x^2 - 8x - 21}\)
isw for incorrect denominator expansion