Answer
$\frac{11}{n-2}$
Work Step by Step
Given \begin{equation}
\frac{n+6}{n-2}+\frac{n-5}{2-n}.
\end{equation} First rewrite the second fraction: \begin{equation}
\frac{n-5}{2-n}= -\frac{n-5}{n-2}
\end{equation} Find the LCM of the fractions which is: $\mathbf{L C M}=n-2$. Perform addition:
\begin{equation}
\begin{aligned}
\frac{n+6}{n-2}+\frac{n-5}{2-n}&=\frac{n+6}{n-2}-\frac{n-5}{n-2} \\
&= \frac{n+6-n+5}{n-2}\\
&= \frac{11}{n-2}.
\end{aligned}
\end{equation} The solution is \begin{equation}
\frac{n+6}{n-2}+\frac{n-5}{2-n}=\frac{11}{n-2}.
\end{equation}
