Problem

$$\mathrm{f}(x)=\frac{5x+10}{(1-x)(2+3x)}$$

(a) Write $\mathrm{f}(x)$ in partial fraction form.

(b) (i) Hence find, in ascending powers of $x$ up to and including the terms in $x^2$, the binomial series expansion of $\mathrm{f}(x)$. Give each coefficient as a simplified fraction.

(ii) Find the range of values of $x$ for which this expansion is valid.