4MA0 Higher June 2012 Paper 4 Q21
21 Solve \(\dfrac{5}{(x + 2)} + \dfrac{9}{(x - 2)} = 2\)
Show clear algebraic working.
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{5(x - 2) + 9(x + 2)}{(x + 2)(x - 2)}\) (=2) | M1 |
| \(14x + 8 = 2(x + 2)(x - 2)\) or \(\dfrac{14x + 8}{(x - 2)(x + 2)}\) (=2) | M1 |
| \(2x^2 - 14x - 16\) (= 0) oe \(x^2 - 7x - 8\) (= 0) oe | A1 |
| \((x + 1)(x - 8)\) (= 0) oe | M1 |
| \(x = -1\), \(x = 8\) | A1 |
| (Total 5 marks) |
Notes
M1: correct expression with correct common denominator
or \(5(x - 2) + 9(x + 2) = 2(x + 2)(x - 2)\)
M1: gather terms correctly. Accept \(x^2 - 4\) for \((x + 2)(x - 2)\)
A1: correct 3 part quadratic
M1: or \(\dfrac{7 \pm \sqrt{7^2 - 4 \times 1 \times -8}}{2}\) oe condone 1 sign error
A1: dep on previous M1