Question

Add and express the answer in lowest terms.
StartFraction 15 Over f minus 8 EndFraction plus StartFraction 1 Over 8 minus f EndFraction

Answer 1

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:

\[
\frac{14}{f - 8}
\]