Answer
$\frac{11}{x-5}$
Work Step by Step
Given \begin{equation}
\frac{x-7}{5-x}+\frac{x+4}{x-5}.
\end{equation} First rewrite the first fraction:
\begin{equation}
\frac{x-7}{5-x}= -\frac{x-7}{x-5}= \frac{-x+7}{x-5}.
\end{equation} Find the LCD of the fractions which is: $\mathbf{LCD}=x-5$.
\begin{equation}
\begin{aligned}
\frac{x-7}{5-x}+\frac{x+4}{x-5}&=\frac{-x+7}{x-5}+\frac{x+4}{x-5} \\
&= \frac{11}{x-5}.
\end{aligned}
\end{equation}
