6 Let \(f ( x ) = \frac { 6 + 7 x } { ( 2 - x ) \left( 1 + x ^ { 2 } \right) }\).
- Express \(\mathrm { f } ( x )\) in partial fractions.
- Show that, when \(x\) is sufficiently small for \(x ^ { 4 }\) and higher powers to be neglected,
$$f ( x ) = 3 + 5 x - \frac { 1 } { 2 } x ^ { 2 } - \frac { 15 } { 4 } x ^ { 3 }$$