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