Generalised Binomial Theorem and Partial Fractions
9
Express \(\frac { 4 + 12 x + x ^ { 2 } } { ( 3 - x ) ( 1 + 2 x ) ^ { 2 } }\) in partial fractions.
Hence obtain the expansion of \(\frac { 4 + 12 x + x ^ { 2 } } { ( 3 - x ) ( 1 + 2 x ) ^ { 2 } }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\).