\(\frac{m-4}{2-m^2}< 0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m-4>0\\2-m^2< 0\end{matrix}\right.\\\left\{{}\begin{matrix}m-4< 0\\2-m^2>0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}\left\{{}\begin{matrix}m>4\\m< \sqrt{2}\end{matrix}\right.\\\left\{{}\begin{matrix}m< 4\\m>\sqrt{2}\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\sqrt{2}< m< 4\)(1)
\(\frac{m-2m^2}{4-2m^2}>0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m-2m^2>0\\4-2m^2>0\end{matrix}\right.\\\left\{{}\begin{matrix}m-2m^2< 0\\m-2m^2< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m< \sqrt{2}\\m\left(1-2m\right)>0\end{matrix}\right.\\\left\{{}\begin{matrix}m>\sqrt{2}\\m\left(1-2m\right)< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m< \sqrt{2}\\\left[{}\begin{matrix}\left\{{}\begin{matrix}m>0\\1-2m>0\end{matrix}\right.\\\left\{{}\begin{matrix}m< 0\\1-2m< 0\end{matrix}\right.\end{matrix}\right.\end{matrix}\right.\\\left\{{}\begin{matrix}m>\sqrt{2}\\\left[{}\begin{matrix}\left\{{}\begin{matrix}m>0\\1-2m< 0\end{matrix}\right.\\\left\{{}\begin{matrix}m< 0\\1-2m>0\end{matrix}\right.\end{matrix}\right.\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m< \sqrt{2}\\\left\{{}\begin{matrix}m>0\\m< \frac{1}{2}\end{matrix}\right.\end{matrix}\right.\\\left\{{}\begin{matrix}m>\sqrt{2}\\m>\frac{1}{2}\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}0< m< \frac{1}{2}\\m>\sqrt{2}\end{matrix}\right.\) (2)
\(\underrightarrow{\left(1\right)\left(2\right)}\) \(\sqrt{2}< m< \frac{1}{2}\)
