Express $$\frac{5(x - 3)}{(2x - 11)(4 - 3x)}$$ in the form $$\frac{A}{(2x - 11)} + \frac{B}{(4 - 3x)}$$ where A and B are integers. - AQA - A-Level Maths Mechanics - Question 5 - 2021 - Paper 2

To find A and B, we can select an appropriate value for x. Let's substitute $x = \frac{4}{3}$ into the equation:

$5\left(\frac{4}{3} - 3\right) \equiv A(4 - 3 \cdot \frac{4}{3}) + B(2 \cdot \frac{4}{3} - 11).$ This simplifies to (5(-\frac{5}{3}) \equiv A(0) + B(-\frac{5}{3})$$ which gives us A = -1 after solving for it.

Next, let's substitute $x = \frac{11}{2}$ into the original equation:

$5\left(\frac{11}{2} - 3\right) \equiv A(4 - 3 \cdot \frac{11}{2}) + B(2 \cdot \frac{11}{2} - 11).$ After simplification, we find that A = -1 leads to B = 1 after appropriate calculations.