\(1,P=\left(\dfrac{1}{x+\sqrt{x}}-\dfrac{1}{\sqrt{x}+1}\right):\dfrac{\sqrt{x}}{x+2\sqrt{x}+1}\left(đk:x>0\right)\)
\(=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}+1\right)}-\dfrac{1}{\sqrt{x}+1}\right):\dfrac{\sqrt{x}}{\left(\sqrt{x}+1\right)^2}\)
\(=\left(\dfrac{1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\right).\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}}\)
\(=\dfrac{\left(1-\sqrt{x}\right)\left(\sqrt{x}+1\right)}{\sqrt{x}^2}\)
2.
\(P=\dfrac{1-x}{x}=\dfrac{1}{x}-1\)
\(P\in Z\Leftrightarrow\dfrac{1}{x}\in Z\)
\(\Rightarrow x=Ư\left(1\right)\)
\(\Rightarrow x=1\) (do \(x>0\))
