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A=a= ( ( sqrt(a))/( sqrt(a)-1) - ( sqrt(a))/(a- sqrt(a)) )/( ( sqrt(a)+1)/(a-1) )
\(A=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}}{a-\sqrt{a}}\right):\dfrac{\sqrt{a}+1}{a-1}\left(a>0;a\ne1\right)\\ =\left[\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\right]:\dfrac{\sqrt{a}+1}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\\ =\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}-1}\right):\dfrac{1}{\sqrt{a}-1}\\ =\dfrac{\sqrt{a}-1}{\sqrt{a}-1}:\dfrac{1}{\sqrt{a}-1}\\ =1:\dfrac{1}{\sqrt{a}-1}\\ =\sqrt{a}-1\)
\(A=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}}{a-\sqrt{a}}\right):\dfrac{\sqrt{a}+1}{a-1}\left(a>0;a\ne1\right)\\ =\left[\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\right]:\dfrac{\sqrt{a}+1}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\\ =\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}-1}\right):\dfrac{1}{\sqrt{a}-1}\\ =\dfrac{\sqrt{a}-1}{\sqrt{a}-1}:\dfrac{1}{\sqrt{a}-1}\\ =1:\dfrac{1}{\sqrt{a}-1}\\ =\sqrt{a}-1\)