OCR C4 — Question 3

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
TopicGeneralised Binomial Theorem and Partial Fractions

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