Answer
$\frac{15}{x-9}$
Work Step by Step
Given \begin{equation}
\frac{x+7}{x-9}+\frac{x-8}{9-x}.
\end{equation} First rewrite the second fraction:
\begin{equation}
\frac{x-8}{9-x}= -\frac{x-8}{x-9}= \frac{-x+8}{x-9}.
\end{equation} Find the LCD of the fractions which is: $\mathbf{LCD}=x-9$.
\begin{equation}
\begin{aligned}
\frac{x+7}{x-9}+\frac{x-8}{9-x}&=\frac{x+7}{x-9}+\frac{-x+8}{x-9} \\
&= \frac{15}{x-9}.
\end{aligned}
\end{equation}
