Higher June 2022 Unit 2 Q12
12. Express the following as a single fraction in its simplest form. [3]
\[\frac{4}{3x - 7} + \frac{5}{2x + 9}\]| Scheme | Marks | Comments |
|---|---|---|
| \(4\,(2x + 9) + 5\,(3x - 7)\) [\(= 8x + 36 + 15x - 35\)] as a numerator within a single fraction | M1 | Accept intention of brackets. e.g. \(4 \times 2x + 9 + 5 \times 3x - 7\) |
| \((3x - 7)\,(2x + 9)\) as a denominator | M1 | |
| \(= \dfrac{23x + 1}{(3x - 7)(2x + 9)}\) or \(\dfrac{23x + 1}{6x^2 + 13x - 63}\) | A1 | CAO. Mark final answer. (If expanded, the denominator must be correct.) If no marks awarded, then SC1 for sight of \(23x + 1\). |