To add the fractions \(\frac{15}{f - 8}\) and \(\frac{1}{8 - f}\), we first notice that \(8 - f\) can be rewritten as \(-(f - 8)\). Therefore, we can express the second fraction as follows:
\[ \frac{1}{8 - f} = \frac{1}{-(f - 8)} = -\frac{1}{f - 8} \]
Now we can rewrite the original expression:
\[ \frac{15}{f - 8} + \frac{1}{8 - f} = \frac{15}{f - 8} - \frac{1}{f - 8} \]
Now that both fractions have a common denominator, we can combine them:
\[ \frac{15 - 1}{f - 8} = \frac{14}{f - 8} \]
Thus, the simplified expression in lowest terms is:
\[ \frac{14}{f - 8} \]