Consider the function $f : ( - \infty , \infty ) \rightarrow ( - \infty , \infty )$ defined by
$$f ( x ) = \frac { x ^ { 2 } - a x + 1 } { x ^ { 2 } + a x + 1 } , 0 < a < 2 .$$
Which of the following is true?\\
(A) $( 2 + a ) ^ { 2 } f ^ { \prime \prime } ( 1 ) + ( 2 - a ) ^ { 2 } f ^ { \prime \prime } ( - 1 ) = 0$\\
(B) $( 2 - a ) ^ { 2 } f ^ { \prime \prime } ( 1 ) - ( 2 + a ) ^ { 2 } f ^ { \prime \prime } ( - 1 ) = 0$\\
(C) $f ^ { \prime } ( 1 ) f ^ { \prime } ( - 1 ) = ( 2 - a ) ^ { 2 }$\\
(D) $f ^ { \prime } ( 1 ) f ^ { \prime } ( - 1 ) = - ( 2 + a ) ^ { 2 }$