Find the Exact Value Under the Given Conditions Find $\tan ( \alpha + \beta )$

Multiple Choice

Find the exact value under the given conditions.
- $\cos \alpha = - \frac { 24 } { 25 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = - \frac { \sqrt { 21 } } { 5 } , \pi < \beta < \frac { 3 \pi } { 2 } \quad$ Find $\tan ( \alpha + \beta )$

A) $\frac { - 14 + 24 \sqrt { 21 } } { 48 + 7 \sqrt { 21 } }$
B) $\frac { 48 + 7 \sqrt { 21 } } { - 14 + 24 \sqrt { 21 } }$
C) $\frac { 14 - 24 \sqrt { 21 } } { 48 + 7 \sqrt { 21 } }$
D) $\frac { - 14 + 24 \sqrt { 21 } } { 125 }$