Simplification then binomial expansion

A question is this type if and only if it requires first simplifying an algebraic expression (combining fractions or other operations) before applying binomial expansion.

1 questions · Standard +0.3

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OCR C4 Q3
9 marks Standard +0.3
$$f(x) = 3 - \frac{x-1}{x-3} + \frac{x+11}{2x^2-5x-3}, \quad |x| < \frac{1}{2}.$$
  1. Show that $$f(x) = \frac{4x-1}{2x+1}.$$ [4]
  2. Find the series expansion of \(f(x)\) in ascending powers of \(x\) up to and including the term in \(x^3\), simplifying each coefficient. [5]