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 Pure - Question 5 - 2021 - Paper 2

To find A, we can substitute a convenient value for x.

Letting ( x = \frac{4}{3} ), the equation simplifies as follows:

$5\left(\frac{4}{3} - 3\right) = A(4 - 3\left(\frac{4}{3}\right)) + B(2\left(\frac{4}{3}\right) - 11)$.

Simplifying, we find: ( A = -1 ).

Next, to find B, we substitute a different value for x.

Letting ( x = \frac{11}{2} ), we again simplify:

$5\left(\frac{11}{2} - 3\right) = A(4 - 3\left(\frac{11}{2}\right)) + B(2\left(\frac{11}{2}\right) - 11)$.

Which results in:\n( B = 1 ).