7.
$$f ( x ) = \frac { 4 x - 5 } { ( 2 x + 1 ) ( x - 3 ) } - \frac { 2 x } { x ^ { 2 } - 9 } , \quad x \neq \pm 3 , x \neq - \frac { 1 } { 2 }$$
- 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 \(C\).
- Find an equation of the normal to \(C\) at \(P\).