(i)[4]
Write $f(x)$ in the form $\dfrac{A}{3 - x} + \dfrac{Bx + C}{2 + x^2}$.
(ii)[5]
Hence find the expansion of $f(x)$ in ascending powers of $x$, up to and including the term in $x^3$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
Define $f(x) = \dfrac{x - 4x^2}{(3 - x)(2 + x^2)}$.