Find the Partial Fraction Expansion of the Rational Function $\frac { x ^ { 2 } } { ( x - 1 ) \left( x ^ { 2 } + 1 \right) }$

Multiple Choice

Find the partial fraction expansion of the rational function: $\frac { x ^ { 2 } } { ( x - 1 ) \left( x ^ { 2 } + 1 \right) }$ .

A) $\frac { 1 } { 2 ( x - 1 ) } + \frac { 1 } { 2 \left( x ^ { 2 } + 1 \right) }$
B) $\frac { 1 } { 2 ( x - 1 ) } + \frac { x } { 2 \left( x ^ { 2 } + 1 \right) }$
C) $\frac { 1 } { ( x - 1 ) } + \frac { x + 1 } { \left( x ^ { 2 } + 1 \right) }$
D) $\frac { 1 } { ( x - 1 ) } + \frac { 1 } { \left( x ^ { 2 } + 1 \right) }$
E) $\frac { 1 } { 2 ( x - 1 ) } + \frac { x + 1 } { 2 \left( x ^ { 2 } + 1 \right) }$
F) $\frac { - 1 } { 2 ( x - 1 ) } + \frac { x + 1 } { 2 \left( x ^ { 2 } + 1 \right) }$
G) $\frac { 1 } { ( x - 1 ) } + \frac { x } { \left( x ^ { 2 } + 1 \right) }$
H) $\frac { 1 } { 2 ( x - 1 ) } - \frac { x + 1 } { 2 \left( x ^ { 2 } + 1 \right) }$