\(A=\frac{x}{x-1}-\frac{\sqrt{x}\left(2\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{x}{x-1}-\frac{2\sqrt{x}-1}{\sqrt{x}-1}=\frac{x}{x-1}-\frac{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{x}{x-1}-\frac{2x+\sqrt{x}-1}{x-1}=\frac{\sqrt{x}-x-1}{x-1}\)
\(x=3+2\sqrt{2}\Rightarrow\sqrt{x}=\sqrt{3+2\sqrt{2}}=\sqrt{2+2\sqrt{2}+1}=\sqrt{\left(\sqrt{2}+1\right)^2}=\sqrt{2}+1\Rightarrow A=\frac{\sqrt{2}-3-2\sqrt{2}}{2+2\sqrt{2}}=\frac{-3-\sqrt{2}}{2+2\sqrt{2}}\)
Điều kiện : \(\left\{{}\begin{matrix}x >0\\x\ne1\end{matrix}\right.\)
A = \(\frac{x}{x-1}-\frac{2x-\sqrt{x}}{x-\sqrt{x}}=\frac{x}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\frac{\sqrt{x}\left(2\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
= \(\frac{x}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\frac{1-2\sqrt{x}}{\sqrt{x}-1}=\frac{x+\left(1-2\sqrt{x}\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
= \(\frac{x+\left(\sqrt{x}+1-2x-2\sqrt{x}\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{x+\sqrt{x}+1-2x-2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
=\(\frac{1-x-\sqrt{x}}{x-1}\)
