Solve the Problem A) $g ( x ) = \frac { x + 4 } { x + 6 }$

Multiple Choice

Solve the problem.
- $\text { Given } f ( x ) = \frac { 1 } { x } \text { and } \left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x } \text {, find the function } g \text {. }$

A) $g ( x ) = \frac { x + 4 } { x + 6 }$
B) $g ( x ) = \frac { x + 6 } { x + 4 }$
C) $g ( x ) = \frac { x - 4 } { x - 6 }$
D) $g ( x ) = \frac { x - 6 } { x - 4 }$