\(A=\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}-\dfrac{1}{\sqrt{a}}\right)\);\(\left\{{}\begin{matrix}a\ge0\\a\ne1\end{matrix}\right.\)
\(A=\left(\dfrac{\left(\sqrt{a}+1\right)^2-\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+4\sqrt{a}\right)\left(\dfrac{a-1}{\sqrt{a}}\right)\)
\(A=\left(\dfrac{4\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+4\sqrt{a}\right)\left(\dfrac{a-1}{\sqrt{a}}\right)\)
\(A=4\sqrt{a}\left(\dfrac{1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\left(\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a}}\right)\)
\(A=4\)
