4MA0 Higher January 2015 Paper 4 Q23
23 Write \(5 - (x + 2) \div \left(\dfrac{x^2 - 4}{x - 3}\right)\) as a single fraction.
Simplify your answer fully.
(4)
| Scheme | Marks |
|---|---|
| \(x^2 - 4 = (x + 2)(x - 2)\) | B1 |
\([5 -](x + 2) \times \dfrac{(x - 3)}{(x^2 - 4)}\) or \([5 -](x + 2) \times \dfrac{(x - 3)}{(x - 2)(x + 2)}\) | M1 |
\(\dfrac{5(x - 2)}{(x - 2)} - \dfrac{(x - 3)}{(x - 2)}\) or \(\dfrac{5(x - 2)(x + 2)}{(x - 2)(x + 2)} - (x + 2) \times \dfrac{(x - 3)}{(x - 2)(x + 2)}\) or \(\dfrac{5(x^2 - 4)}{x^2 - 4} - (x + 2) \times \dfrac{(x - 3)}{x^2 - 4}\) | M1 |
| \(\dfrac{4x - 7}{x - 2}\) | A1 |
| (4 marks) |
Notes
B1: independent
M1: for dealing with division of \((x + 2)\) by \(\dfrac{x^2 - 4}{x - 3}\)
M1: For two correct fractions with a common denominator or a correct single fraction
A1: from fully correct algebra