Consider $f(x) = \frac{3a - 5x}{(3a + 2x)(2a - x)}$, where $a$ is a positive constant.
(a)[3]
Express $f(x)$ in the form of partial fractions.
(b)[4]
Hence find the expansion of $f(x)$ as a series in ascending powers of $x$, up to and including the term in $x^2$.
(c)[1]
State the values of $x$ for which the expansion in part (b) remains valid.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Form the partial-fraction decomposition $\frac{A}{3a+2x}+\frac{B}{2a-x}$” …