\(\dfrac{4x}{\sqrt{x}-3}>0\) (\(\sqrt{x}-3\) có nghĩa khi \(x\ge0\)) (1)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}4x>0\Leftrightarrow x>0\left(2\right)\\\sqrt{x}-3>0\Leftrightarrow\left\{{}\begin{matrix}x>9\left(3\right)\\x< -9\left(KTMĐKx\ge0\right)\left(4\right)\end{matrix}\right.\end{matrix}\right.\\\left\{{}\begin{matrix}4x< 0\Leftrightarrow x< 0\left(5\right)\\\sqrt{x}-3< 0\Leftrightarrow\left\{{}\begin{matrix}x< 9\left(6\right)\\x>-9\left(7\right)\end{matrix}\right.\end{matrix}\right.\end{matrix}\right.\)
Từ \(\left(1\right),\left(2\right),\left(3\right),\left(4\right)\)suy ra \(x>9\left(8\right)\)
Từ \(\left(1\right),\left(5\right),\left(6\right),\left(7\right)\) suy ra \(0\le x< 9\left(9\right)\)
Từ \(\left(8\right),\left(9\right)\) suy ra \(\dfrac{4x}{\sqrt{x}-3}>0\) khi \(x\ge0\)
