\(=\left(\dfrac{\sqrt{a}\left(\sqrt{a}+2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}+\dfrac{\sqrt{a}\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\right):\dfrac{2\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)
\(=\left(\dfrac{a+2\sqrt{a}+a-2\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\right):\dfrac{2\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)
\(=\dfrac{2a}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}.\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{2\sqrt{a}}\)
\(=\sqrt{a}\)
\(\left(\dfrac{\sqrt{a}}{\sqrt{a}-2}+\dfrac{\sqrt{a}}{\sqrt{a}+2}\right):\dfrac{\sqrt{4a}}{a-4}\\ =\left(\dfrac{\sqrt{a}.\left(\sqrt{a}+2\right)+\sqrt{a}.\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\right):\dfrac{\sqrt{4a}}{a-4}\\ =\left(\dfrac{a+2\sqrt{a}+a-2\sqrt{a}}{a-4}\right):\dfrac{\sqrt{4a}}{a-4}\\ =\dfrac{2a}{a-4}.\dfrac{a-4}{\sqrt{4a}}\\ =\dfrac{2a}{2a}=1\)
\(\left(\dfrac{\sqrt{a}}{\sqrt{a}-2}+\dfrac{\sqrt{a}}{\sqrt{a}+2}\right):\dfrac{\sqrt{4a}}{a-4}=\dfrac{\sqrt{a}\left(\sqrt{a}+2+\sqrt{a}-2\right)}{\left(\sqrt{a}+2\right)\left(\sqrt{a-2}\right)}\cdot\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a-2}\right)}{2\sqrt{a}}\)\(=\dfrac{2\sqrt{a}}{2}=\sqrt{a}\) `(a ne 4 , a>0)`
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