Simplify the Rational Expression A) $\frac { ( 4 x ) \left( 1 + 15 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
- $$\frac { \left( x ^ { 2 } + 1 \right) ^ { 4 } ( 4 x ) - x ^ { 2 } ( 16 ) \left( x ^ { 2 } + 1 \right) ^ { 3 } ( 4 x ) } { \left( x ^ { 2 } + 1 \right) ^ { 8 } }$$

A) $\frac { ( 4 x ) \left( 1 + 15 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$

B) $\frac { ( 4 x ) \left( 1 - 15 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$

C) $\frac { ( 4 x ) \left( 1 - 17 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$

D) $\frac { ( 4 x ) \left( 1 + 17 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$