Perform the Indicated Operations and Simplify the Result $$\frac { x ^ { 2 } + 12 x + 27 } { x ^ { 2 } + 16 x + 63 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 7 x + 12 }$$

Multiple Choice

Perform the indicated operations and simplify the result. Leave the answer in factored form.
- $$\frac { x ^ { 2 } + 12 x + 27 } { x ^ { 2 } + 16 x + 63 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 7 x + 12 }$$

A) $\frac { 1 } { x + 4 }$
B) $\frac { x } { x + 4 }$
C) $\frac { x } { x ^ { 2 } + 16 x + 63 }$
D) $\frac { x ^ { 2 } + 7 x } { x + 4 }$