Edexcel C3 2014 January — Question 2

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2014
SessionJanuary
TopicPolynomial Division & Manipulation

2. $$f ( x ) = \frac { 15 } { 3 x + 4 } - \frac { 2 x } { x - 1 } + \frac { 14 } { ( 3 x + 4 ) ( x - 1 ) } , \quad x > 1$$
  1. Express \(\mathrm { f } ( x )\) as a single fraction in its simplest form.
  2. Hence, or otherwise, find \(\mathrm { f } ^ { \prime } ( x )\), giving your answer as a single fraction in its simplest form.