Ta có: \(\left(\frac{\sqrt{x}}{3-\sqrt{x}}+\frac{x-9}{9-x}\right):\left(\frac{3\sqrt{x}+1}{x-3\sqrt{x}}-\frac{1}{\sqrt{x}}\right)\)
\(=\left(\frac{-\sqrt{x}}{\sqrt{x}-3}-\frac{x-9}{x-9}\right):\left(\frac{3\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}-3}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\frac{-\sqrt{x}}{\sqrt{x}-3}-1\right):\left(\frac{3\sqrt{x}+1-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\frac{-\sqrt{x}}{\sqrt{x}-3}-\frac{\sqrt{x}-3}{\sqrt{x}-3}\right):\left(\frac{2\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\frac{-\sqrt{x}-\sqrt{x}+3}{\sqrt{x}-3}\right)\cdot\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\sqrt{x}+4}\)
\(=\frac{-2\sqrt{x}+3}{\sqrt{x}-3}\cdot\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\sqrt{x}+4}\)
\(=\frac{-2x+3\sqrt{x}}{2\sqrt{x}+4}\)
