\(\left(x-1\right)\left(x+2\right)< 0\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\Rightarrow x>1\\x+2< 0\Rightarrow x< -2\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\Rightarrow x< 1\\x+2>0\Rightarrow x>-2\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow-2< x< 1\)