\(\frac{2}{a}-\frac{2-a}{a\sqrt{a}+a}=\frac{2}{a}-\frac{2-a}{a\left(\sqrt{a}+1\right)}=\frac{2\left(\sqrt{a}+1\right)-2+a}{a\sqrt{a}+a}=\frac{2\sqrt{a}+a}{\sqrt{a}\left(a+\sqrt{a}\right)}=\frac{\sqrt{a}\left(2+\sqrt{a}\right)}{\sqrt{a}\left(a+\sqrt{a}\right)}=\frac{2+\sqrt{a}}{a+\sqrt{a}}\)
\(\frac{2}{a}\)-\(\frac{2-a}{a\sqrt{a}+a}\)=\(\frac{2}{a}\)-\(\frac{2-a}{a\left(\sqrt{a}+1\right)}\)=\(\frac{2\left(\sqrt{a}+1\right)}{a\left(\sqrt{a}+1\right)}\)-\(\frac{2-a}{a\left(\sqrt{a}+1\right)}\)=\(\frac{2\sqrt{a}+2-2+a}{a\left(\sqrt{a}+1\right)}\)=\(\frac{2\sqrt{a}+a}{a\left(\sqrt{a}+1\right)}\)=\(\frac{\sqrt{a}\left(\sqrt{a}+2\right)}{a\left(\sqrt{a}+1\right)}\)=\(\frac{\sqrt{a}+2}{\sqrt{a}\left(\sqrt{a}+1\right)}\)
