\(\left(x^2-x-2\right)\left(x^2+x\right)< 0\)
TH1: \(\left\{{}\begin{matrix}x^2-x-2< 0\\x^2+x>0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left(x-2\right)\left(x+1\right)< 0\\x\left(x+1\right)>0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-1< x< 2\\\left[{}\begin{matrix}x>0\\x< -1\end{matrix}\right.\end{matrix}\right.\)
=>\(0< x< 2\)
TH2: \(\left\{{}\begin{matrix}x^2-x-2>0\\x^2+x< 0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left(x-2\right)\left(x+1\right)>0\\x\left(x+1\right)< 0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left[{}\begin{matrix}x>2\\x< -1\end{matrix}\right.\\-1< x< 0\end{matrix}\right.\Leftrightarrow x\in\varnothing\)