#andy
\[\begin{array}{l}
\frac{{x - 3}}{{x + 1}} > 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 3 > 0,\,\,x + 1 > 0\\
x - 3 < 0,\,\,x + 1 < 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x > 3\\
x < - 1
\end{array} \right.
\end{array}\]