1.
$$f ( x ) = \frac { 5 x + 10 } { ( 1 - x ) ( 2 + 3 x ) }$$
- Write \(\mathrm { f } ( x )\) in partial fraction form.
- 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.
- Find the range of values of \(x\) for which this expansion is valid.