Edexcel C3 2011 June — Question 7

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2011
SessionJune
TopicPartial Fractions
TypeTangent or normal to curve

7. $$f ( x ) = \frac { 4 x - 5 } { ( 2 x + 1 ) ( x - 3 ) } - \frac { 2 x } { x ^ { 2 } - 9 } , \quad x \neq \pm 3 , x \neq - \frac { 1 } { 2 }$$
  1. Show that $$f ( x ) = \frac { 5 } { ( 2 x + 1 ) ( x + 3 ) }$$ The curve \(C\) has equation \(y = \mathrm { f } ( x )\). The point \(P \left( - 1 , - \frac { 5 } { 2 } \right)\) lies on \(C\).
  2. Find an equation of the normal to \(C\) at \(P\).