Generalised Binomial Theorem and Partial Fractions
8
Given that \(\frac { 3 x + 4 } { ( 1 + x ) ( 2 + x ) ^ { 2 } } \equiv \frac { A } { 1 + x } + \frac { B } { 2 + x } + \frac { C } { ( 2 + x ) ^ { 2 } }\), find \(A , B\) and \(C\).
Hence or otherwise expand \(\frac { 3 x + 4 } { ( 1 + x ) ( 2 + x ) ^ { 2 } }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\).
State the set of values of \(x\) for which the expansion in part (ii) is valid.