Higher January 2020 Paper 2 Q24
24 Express
\[\left(\dfrac{4}{2x - 5} - \dfrac{3}{2x - 3}\right) \div \dfrac{9x - 4x^3}{6x^2 - 17x + 5}\]
as a single fraction in its simplest form.
(4)
| Scheme | Marks |
|---|---|
| \(\dfrac{4(2x - 3) - 3(2x - 5)}{(2x - 5)(2x - 3)}\) or \(\dfrac{8x - 12 - 6x + 15}{(2x - 5)(2x - 3)}\) oe | M1 |
| \(x(3 - 2x)(3 + 2x)\) or \((3x - 1)(2x - 5)\) | M1 |
| \(\dfrac{2x + 3}{(2x - 5)(2x - 3)} \times \dfrac{(3x - 1)(2x - 5)}{x(3 - 2x)(3 + 2x)}\) | M1 |
| \(\dfrac{3x - 1}{x(2x - 3)(3 - 2x)}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: Writing 1st fraction as a fraction over a common denominator (can be 2 separate fractions)
M1: Complete factorisation of numerator or denominator of 2nd fraction
M1: may be partially simplified
A1: e.g.
\(\dfrac{3x - 1}{x(2x - 3)(3 - 2x)}\) or
\(\dfrac{1 - 3x}{x(2x - 3)^2}\) or
\(\dfrac{3x - 1}{x(12x - 9 - 4x^2)}\) or
\(\dfrac{3x - 1}{(12x^2 - 9x - 4x^3)}\) oe
isw for incorrect denominator expansion