Find All Values of X Satisfying the Given Conditions $y _ { 1 } = \frac { 1 } { x + 4 } , y _ { 2 } = \frac { 1 } { x + 3 } , y _ { 3 } = \frac { - 1 } { x ^ { 2 } + 7 x + 12 }$

Multiple Choice

Find all values of x satisfying the given conditions.
- $y _ { 1 } = \frac { 1 } { x + 4 } , y _ { 2 } = \frac { 1 } { x + 3 } , y _ { 3 } = \frac { - 1 } { x ^ { 2 } + 7 x + 12 }$ , and the sum of $y _ { 1 }$ and 2 times $y _ { 2 }$ is $y _ { 3 }$ .

A) $\{ - 4 \}$
B) $\{ 0 \}$
C) $\{ 3 \}$
D) $\varnothing$