Generalised Binomial Theorem and Partial Fractions
9
Express \(\frac { 2 - x + 8 x ^ { 2 } } { ( 1 - x ) ( 1 + 2 x ) ( 2 + x ) }\) in partial fractions.
Hence obtain the expansion of \(\frac { 2 - x + 8 x ^ { 2 } } { ( 1 - x ) ( 1 + 2 x ) ( 2 + x ) }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\).