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