Generalised Binomial Theorem and Partial Fractions
8
Express \(\frac { 5 x + 3 } { ( x + 1 ) ^ { 2 } ( 3 x + 2 ) }\) in partial fractions.
Hence obtain the expansion of \(\frac { 5 x + 3 } { ( x + 1 ) ^ { 2 } ( 3 x + 2 ) }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), simplifying the coefficients.