\(x\left(x-2\right)< 0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\\x-2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x>0\\x-2< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x>0\\x< 2\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\in\varnothing\\x\in\left(0;2\right)\end{matrix}\right.\)
Vậy \(x\in\left(0;2\right)\) thỏa mãn.
\(x\left(x-2\right)>0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\\x-2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x< 0\\x-2< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x< 0\\x< 2\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\in\left(2;+\infty\right)\\x\in\left(-\infty;0\right)\end{matrix}\right.\)
Vậy \(x\in\left(2;+\infty\right)\cup\left(2;+\infty\right)\) thỏa mãn.
\(\left(x-1\right)\left(x+3\right)>0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\x+3>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\x+3< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x>3\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x< 3\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\in\left(1;+\infty\right)\\x\in\left(-\infty;-3\right)\end{matrix}\right.\)
Vậy.....
\(\left(x-1\right)\left(x+3\right)< 0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1< 0\\x+3>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1>0\\x+3< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 1\\x>-3\end{matrix}\right.\\\left\{{}\begin{matrix}x>1\\x< -3\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\in\left(3-;1\right)\\x\in\varnothing\end{matrix}\right.\)
Vậy....
