\(P=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{x-\sqrt{x}}\right):\dfrac{\sqrt{x}+1}{3}\)
\(\Rightarrow P=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\right).\dfrac{3}{\sqrt{x}+1}\)
\(\Rightarrow P=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}-1}\right).\dfrac{3}{\sqrt{x}+1}\)
\(\Rightarrow P=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}.\dfrac{3}{\sqrt{x}+1}\)
\(\Rightarrow P=\dfrac{3}{\sqrt{x}-1}\)