2. Given that
$$\frac { 3 x ^ { 2 } + 4 x - 7 } { ( x + 1 ) ( x - 3 ) } \equiv A + \frac { B } { x + 1 } + \frac { C } { x - 3 }$$
- find the values of the constants \(A , B\) and \(C\).
- Hence, or otherwise, find the series expansion of
$$\frac { 3 x ^ { 2 } + 4 x - 7 } { ( x + 1 ) ( x - 3 ) } \quad | x | < 1$$
in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\)
Give each coefficient as a simplified fraction.