\(A=\frac{1}{\sqrt{x-1}-\sqrt{x}}+\frac{1}{\sqrt{x-1}+\sqrt{x}}+\frac{\sqrt{x^3}-x}{\sqrt{x}-1}\)(ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x\ne1\end{matrix}\right.\))
\(=\frac{\sqrt{x-1}+\sqrt{x}+\sqrt{x-1}-\sqrt{x}}{x-1-x}+\frac{x\sqrt{x}-x}{\sqrt{x}-1}\)(vì \(x\ge0\))
\(=-2\sqrt{x-1}+\frac{x\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)
\(=x-2\sqrt{x-1}\)