5. Let
$$f ( x ) = \frac { 27 x ^ { 2 } + 32 x + 16 } { ( 3 x + 2 ) ^ { 2 } ( 1 - x ) }$$
- Express \(f ( x )\) in terms of partial fractions
- Hence, or otherwise, find the series expansion of \(\mathrm { f } ( x )\), in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\). Simplify each term.
- State, with a reason, whether your series expansion in part (b) is valid for \(x = \frac { 1 } { 2 }\).
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