Ta có: \(\left(\frac{x}{x+3\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+3}\right):\left(1-\frac{2}{\sqrt{x}}+\frac{6}{x+3\sqrt{x}}\right)\)
\(=\left(\frac{x}{\sqrt{x}\left(\sqrt{x}+3\right)}+\frac{\sqrt{x}}{\sqrt{x}+3}\right):\left(\frac{x+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}-\frac{2\left(\sqrt{x}+3\right)}{\sqrt{x}\left(\sqrt{x}+3\right)}+\frac{6}{\sqrt{x}\left(\sqrt{x}+3\right)}\right)\)
\(=\frac{2\sqrt{x}}{\sqrt{x}+3}:\frac{x+3\sqrt{x}-2\sqrt{x}-6+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\)
\(=\frac{2\sqrt{x}}{\sqrt{x}+3}:\frac{x-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}\)
\(=\frac{2\sqrt{x}}{\sqrt{x}+3}\cdot\frac{\sqrt{x}\left(\sqrt{x}+3\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(=\frac{2\sqrt{x}}{\sqrt{x}-1}\)
