Edexcel C3 2007 January — Question 2

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2007
SessionJanuary
TopicProof

2. $$f ( x ) = 1 - \frac { 3 } { x + 2 } + \frac { 3 } { ( x + 2 ) ^ { 2 } } , x \neq - 2$$
  1. Show that \(\mathrm { f } ( x ) = \frac { x ^ { 2 } + x + 1 } { ( x + 2 ) ^ { 2 } } , x \neq - 2\).
  2. Show that \(x ^ { 2 } + x + 1 > 0\) for all values of \(x\).
  3. Show that \(\mathrm { f } ( x ) > 0\) for all values of \(x , x \neq - 2\).