a) \(\left(x+1\right)\left(x-2\right)< 0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\\x-2< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1< 0\\x-2>0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-1\\x< 2\end{matrix}\right.\\\left\{{}\begin{matrix}x< -1\\x>2\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-1< x< 2\\x\in\varnothing\end{matrix}\right.\) vậy \(-1< x< 2\)
b) \(\left(x-2\right)\left(x+\dfrac{2}{3}\right)>0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2>0\\x+\dfrac{2}{3}>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-2< 0\\x+\dfrac{2}{3}< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>2\\x>\dfrac{-2}{3}\end{matrix}\right.\\\left\{{}\begin{matrix}x< 2\\x< \dfrac{-2}{3}\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>2\\x< \dfrac{-2}{3}\end{matrix}\right.\) vậy \(x>2\) hoặc \(x< \dfrac{-2}{3}\)