Repeated linear factor with series expansion

Denominator includes a repeated linear factor (squared term); requires expanding terms like (1±ax)^(-2) using binomial series in addition to (1±ax)^(-1).

1 questions · Standard +0.8

1.02y Partial fractions: decompose rational functions
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OCR H240/01 2018 March Q9
11 marks Standard +0.8
9
  1. Express \(\frac { 5 + 4 x - 3 x ^ { 2 } } { ( 1 - 2 x ) ( 2 + x ) ^ { 2 } }\) in three partial fractions.
  2. Hence find the first three terms in the expansion of \(\frac { 5 + 4 x - 3 x ^ { 2 } } { ( 1 - 2 x ) ( 2 + x ) ^ { 2 } }\) in ascending powers of \(x\).
  3. State the set of values for which the expansion in part (ii) is valid.