$$f ( x ) = \frac { 2 x + 3 } { x + 2 } - \frac { 9 + 2 x } { 2 x ^ { 2 } + 3 x - 2 } , \quad x > \frac { 1 } { 2 }$$
- Show that \(\mathrm { f } ( x ) = \frac { 4 x - 6 } { 2 x - 1 }\).
- Hence, or otherwise, find \(\mathrm { f } ^ { \prime } ( x )\) in its simplest form.