Answer
$\frac{2}{x-7}$
Work Step by Step
Given \begin{equation}
\frac{x-1}{7-x}+\frac{x+1}{x-7}.
\end{equation} First rewrite the first fraction:
\begin{equation}
\frac{x-1}{7-x}= -\frac{x-1}{x-7}= \frac{-x+1}{x-7}.
\end{equation} Find the LCD of the fractions which is: $\mathbf{LCD}=x-7$. \begin{equation}
\begin{aligned}
\frac{x-1}{7-x}+\frac{x+1}{x-7}&=\frac{-x+1}{x-7}+\frac{x+1}{x-7} \\
&= \frac{2}{x-7}.
\end{aligned}
\end{equation}
