Standard partial fractions with series expansion

Denominator has distinct linear factors only; expand each partial fraction using standard binomial series (1±x)^(-1) or (1±ax)^(-1).

2 questions

CAIE P3 2015 June Q8
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Hence obtain the expansion of \(\mathrm { f } ( x )\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\). [5]
Edexcel C4 Q11
11. Given that $$\frac { 10 ( 2 - 3 x ) } { ( 1 - 2 x ) ( 2 + x ) } \equiv \frac { A } { 1 - 2 x } + \frac { B } { 2 + x } ,$$
  1. find the values of the constants \(A\) and \(B\).
  2. Hence, or otherwise, find the series expansion in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\), of \(\frac { 10 ( 2 - 3 x ) } { ( 1 - 2 x ) ( 2 + x ) }\), for \(| x | < \frac { 1 } { 2 }\).
    [0pt] [P3 January 2002 Question 3]