5.
$$f ( x ) = \frac { 3 x ^ { 2 } + 16 } { ( 1 - 3 x ) ( 2 + x ) ^ { 2 } } = \frac { A } { ( 1 - 3 x ) } + \frac { B } { ( 2 + x ) } + \frac { C } { ( 2 + x ) ^ { 2 } } , \quad | x | < \frac { 1 } { 3 } .$$
- Find the values of \(A\) and \(C\) and show that \(B = 0\).
- Hence, or otherwise, find the series expansion of \(\mathrm { f } ( x )\), in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\). Simplify each term.