Write the Partial Fraction Decomposition of the Rational Expression $$\frac { - 38 x + 1 } { ( x + 4 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) }$$

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { - 38 x + 1 } { ( x + 4 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) }$$

A) $\frac { 2 } { x + 4 } + \frac { 8 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 x + 1 } { x ^ { 2 } + 1 }$
B) $\frac { 8 x + 1 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 x - 1 } { x ^ { 2 } + 1 }$
C) $\frac { 2 } { x + 4 } + \frac { 9 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 } { x ^ { 2 } + 1 }$
D) $\frac { 2 } { x + 4 } + \frac { 9 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 x - 1 } { x ^ { 2 } + 1 }$