\(y=\frac{x+\sqrt{x}}{x-\sqrt{x}}=\frac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(\Rightarrow y'=\frac{\frac{1}{2\sqrt{x}}\left(\sqrt{x}-1\right)-\left(\sqrt{x}+1\right).\frac{1}{2\sqrt{x}}}{\left(\sqrt{x}-1\right)^2}=\frac{\frac{1}{2\sqrt{x}}\left(\sqrt{x}-1-\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)^2}=-\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)^2}\)