\(1,A=\dfrac{\sqrt{x}-1}{x^2-x}:\left(\dfrac{1}{\sqrt{x}}-\dfrac{1}{\sqrt{x}-1}\right)\left(dk:x>0,x\ne1\right)\)
\(=\dfrac{\sqrt{x}-1}{x\left(x-1\right)}:\dfrac{\sqrt{x}-1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\\ =\dfrac{\sqrt{x}-1}{x\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{-1}\\ =\dfrac{1}{\sqrt{x}\left(\sqrt{x}+1\right)}.\dfrac{\sqrt{x}-1}{-1}\\ =\dfrac{\sqrt{x}-1}{-\sqrt{x}\left(\sqrt{x}+1\right)}\\ =\dfrac{\sqrt{x}-1}{-x-\sqrt{x}}\left(1\right)\)
\(2,x=4+2\sqrt{3}=\left(\sqrt{3}+1\right)^2\left(2\right)\)
Thay \(\left(2\right)\) vào
\(\left(1\right)\Rightarrow A=\dfrac{\sqrt{\left(\sqrt{3}+1\right)^2}-1}{-4-2\sqrt{3}-\sqrt{\left(\sqrt{3}+1\right)^2}}\\
=\dfrac{\sqrt{3}+1-1}{-4-2\sqrt{3}-\sqrt{3}-1}\\
=\dfrac{\sqrt{3}}{-3\sqrt{3}-5}\)
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