# Calculate: (x+1)/(x-5) <= 0

## Expression: $\frac{ x+1 }{ x-5 } \leq 0$

Separate the inequality into two possible cases

$\begin{array} { l }\left\{\begin{array} { l } x+1 \leq 0 \\ x-5 > 0\end{array} \right.,\\\left\{\begin{array} { l } x+1 \geq 0 \\ x-5 < 0\end{array} \right.\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\left\{\begin{array} { l } x \leq -1 \\ x-5 > 0\end{array} \right.,\\\left\{\begin{array} { l } x+1 \geq 0 \\ x-5 < 0\end{array} \right.\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\left\{\begin{array} { l } x \leq -1 \\ x > 5\end{array} \right.,\\\left\{\begin{array} { l } x+1 \geq 0 \\ x-5 < 0\end{array} \right.\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\left\{\begin{array} { l } x \leq -1 \\ x > 5\end{array} \right.,\\\left\{\begin{array} { l } x \geq -1 \\ x-5 < 0\end{array} \right.\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\left\{\begin{array} { l } x \leq -1 \\ x > 5\end{array} \right.,\\\left\{\begin{array} { l } x \geq -1 \\ x < 5\end{array} \right.\end{array}$

Find the intersection

$\begin{array} { l }∅,\\\left\{\begin{array} { l } x \geq -1 \\ x < 5\end{array} \right.\end{array}$

Find the intersection

$\begin{array} { l }∅,\\x \in \left[ -1, 5\right\rangle\end{array}$

Find the union

\begin{align*}&x \in \left[ -1, 5\right\rangle\end{align*}

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