DKXD: \(\left\{{}\begin{matrix}x\ge0\\\sqrt{x}-1\ne0\\x-\sqrt{x}\ne0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt{x}\ne1\\\sqrt{x}\left(\sqrt{x}-1\right)\ne0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt{x}\ne1\\\sqrt{x}\ne0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x>0\\x\ne1\end{matrix}\right.\)
\(A=\left(\dfrac{x+\sqrt{x}}{\sqrt{x}+1}-\dfrac{\sqrt{x}-1}{x-\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{x}\)
\(=\left(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}-\dfrac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right).\dfrac{x}{\sqrt{x}-1}\)
\(=\left(\sqrt{x}-\dfrac{1}{\sqrt{x}}\right).\dfrac{x}{\sqrt{x}-1}\)
\(=\dfrac{\sqrt{x}-1}{\sqrt{x}}.\dfrac{x}{\sqrt{x}-1}\)\(=\dfrac{x}{\sqrt{x}}=\sqrt{x}\)
