ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x\ne9\end{matrix}\right.\)
\(\dfrac{\sqrt{x}}{3\left(\sqrt{x}-3\right)}>=-\dfrac{1}{3}\)
=>\(\dfrac{\sqrt{x}}{\sqrt{x}-3}>=-1\)
=>\(\dfrac{\sqrt{x}}{\sqrt{x}-3}+1>=0\)
=>\(\dfrac{\sqrt{x}+\sqrt{x}-3}{\sqrt{x}-3}>=0\)
=>\(\dfrac{2\sqrt{x}-3}{\sqrt{x}-3}>=0\)
TH1: \(\left\{{}\begin{matrix}2\sqrt{x}-3>=0\\\sqrt{x}-3>0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\sqrt{x}>=\dfrac{3}{2}\\\sqrt{x}>3\end{matrix}\right.\)
=>\(\sqrt{x}>3\)
=>x>9
TH2: \(\left\{{}\begin{matrix}2\sqrt{x}-3< =0\\\sqrt{x}-3< 0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\sqrt{x}< =\dfrac{3}{2}\\\sqrt{x}< 3\end{matrix}\right.\)
=>\(\sqrt{x}< =\dfrac{3}{2}\)
=>\(0< =x< =\dfrac{9}{4}\)
