Đáp án:
\(x \in \left( { - \infty ;\,\,1} \right)\backslash \left\{ { - 1} \right\}\)
Giải thích các bước giải:
\(\begin{array}{l}
\left( {1 - \left| x \right|} \right)\left( {x + 1} \right) > 0\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
1 - \left| x \right| > 0\\
x + 1 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
1 - \left| x \right| < 0\\
x + 1 < 0
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
\left| x \right| < 1\\
x > - 1
\end{array} \right.\\
\left\{ \begin{array}{l}
\left| x \right| > 1\\
x < - 1
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
- 1 < x < 1\\
x > - 1
\end{array} \right.\\
\left\{ \begin{array}{l}
\left[ \begin{array}{l}
x > 1\\
x < - 1
\end{array} \right.\\
x < - 1
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
- 1 < x < 1\\
x < - 1
\end{array} \right..\\
\Rightarrow x \in \left( { - \infty ;\,\,1} \right)\backslash \left\{ { - 1} \right\}.
\end{array}\)
