\(\left(3-x\right)\left(4-x\right)>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3-x< 0\\4-x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}3-x>0\\4-x>0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3< x\\4< x\end{matrix}\right.\\\left\{{}\begin{matrix}3>x\\4>x\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow x\in\varnothing\)