Find the Exact Value of the Expression Using the Provided $\tan ( \mathrm { s } + \mathrm { t } )$

Find the exact value of the expression using the provided information.
-Find $\tan ( \mathrm { s } + \mathrm { t } )$ given that $\cos \mathrm { s } = \frac { 1 } { 3 }$ , with $\mathrm { s }$ in quadrant $\mathrm { I }$ , and $\sin \mathrm { t } = - \frac { 1 } { 2 }$ , with $\mathrm { t }$ in quadrant IV.

A) $\frac { 9 \sqrt { 3 } + 8 \sqrt { 2 } } { 3 }$
B) $\frac { 9 \sqrt { 3 } - 8 \sqrt { 2 } } { 3 }$
C) $\frac { 9 \sqrt { 3 } - 8 \sqrt { 2 } } { 5 }$
D) $\frac { 9 \sqrt { 3 } + 8 \sqrt { 2 } } { 5 }$