9709 P33 - Nov 2023 - Q9
2049
Let \(f(x) = \frac{17x^2 - 7x + 16}{(2 + 3x^2)(2 - x)}\).
(a) Express \(f(x)\) in partial fractions.
(b) Hence obtain the expansion of \(f(x)\) in ascending powers of \(x\), up to and including the term in \(x^3\).
(c) State the set of values of \(x\) for which the expansion in (b) is valid. Give your answer in an exact form.
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