A= (\(\dfrac{\left(a\sqrt{a}-1\right)\cdot\left(a+\sqrt{a}\right)-\left(a\sqrt{a}+1\right)\cdot\left(a-\sqrt{a}\right)}{\left(a-\sqrt{a}\right)\cdot\left(a+\sqrt{a}\right)}\) )\(\cdot\left(\dfrac{\left(\sqrt{a}+1\right)\cdot\left(\sqrt{a}+1\right)+\left(\sqrt{a}-1\right)\cdot\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\cdot\left(\sqrt{a}+1\right)}\right)\)
A = \(\left(\dfrac{a^2\sqrt{a}+a\sqrt{a^2}-a-\sqrt{a}-a^2\sqrt{a}-a\sqrt{a^2}+a+\sqrt{a}}{a^2-\sqrt{a^2}}\right)\) \(\cdot\left[\dfrac{\left(\sqrt{a}+1\right)^2+\left(\sqrt{a}-1\right)^2}{\sqrt{a^2}-1^2}\right]\)
A = \(\left(\dfrac{2a\sqrt{a^2}-2a}{a^2-\sqrt{a^2}}\right)\cdot\left[\dfrac{\left(\sqrt{a}+1\right)^2+\left(\sqrt{a}-1\right)^2}{a-1}\right]\)
A =
\(\left[\dfrac{2\left(a^2-a\right)}{a^2-a}\right]\cdot\left[\dfrac{\left(\sqrt{a}+1\right)^2+\left(\sqrt{a}-1\right)^2}{a-1}\right]\)
A =\(2\cdot\left(\sqrt{a}+1\right)^2\cdot\left(\sqrt{a}-1\right)\)
\(A=\left(\dfrac{a\sqrt{a}-1}{a-\sqrt{a}}-\dfrac{a\sqrt{a}+1}{a+\sqrt{a}}+\sqrt{a}-\dfrac{1}{\sqrt{a}}\right)\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}+\dfrac{\sqrt{a}-1}{\sqrt{a}+1}\right)=\left[\dfrac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}-\dfrac{\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}+1\right)}+\dfrac{a-1}{\sqrt{a}}\right]\left[\dfrac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}+\dfrac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right]\)\(=\left[\dfrac{a+\sqrt{a}+1}{\sqrt{a}}-\dfrac{a-\sqrt{a}+1}{\sqrt{a}}+\dfrac{a-1}{\sqrt{a}}\right]\left[\dfrac{a+2\sqrt{a}+1+a-2\sqrt{a}+1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right]=\dfrac{a+\sqrt{a}+1-a+\sqrt{a}-1+a-1}{\sqrt{a}}.\dfrac{2a+2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}=\dfrac{\left(a+2\sqrt{a}-1\right)\left(2a+2\right)}{\sqrt{a}\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\)