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