Question

12.\(A=\left(\frac{x}{\sqrt{x}-1}-\sqrt{x}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}}-\frac{1}{1-\sqrt{x}}+\frac{2-x}{x-\sqrt{x}}\right)\)

Answer 1

\(A=\left(\frac{x}{\sqrt{x}-1}-\sqrt{x}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}}-\frac{1}{1-\sqrt{x}}+\frac{2-x}{x-\sqrt{x}}\right)\)(\(ĐKXĐ:\left\{{}\begin{matrix}x>0\\x\ne1\end{matrix}\right.\))

\(=\frac{x-x+\sqrt{x}}{\sqrt{x}-1}:\frac{x-1+\sqrt{x}+2-x}{\sqrt{x}\left(\sqrt{x}-1\right)}\)

\(=\frac{\sqrt{x}}{\sqrt{x}-1}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}+1}\)

\(=\frac{x}{\sqrt{x}+1}\)

Answer 2

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