\(C=\dfrac{5+\sqrt{5}}{\sqrt{10}+\sqrt{2}}=\dfrac{\sqrt{5}\left(\sqrt{5}+2\right)}{\sqrt{2}\left(\sqrt{5}+2\right)}=\dfrac{\sqrt{5}}{\sqrt{2}}\)
\(D=\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\dfrac{5-2\sqrt{5}}{2\sqrt{5}-4}=\dfrac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}+\dfrac{\sqrt{5}\left(\sqrt{5}-2\right)}{2\left(\sqrt{5}-2\right)}=\sqrt{5}+\dfrac{\sqrt{5}}{2}=\dfrac{3\sqrt{5}}{2}\)
\(c.\)
\(C=\dfrac{5+\sqrt{5}}{\sqrt{10}+\sqrt{2}}=\dfrac{\sqrt{5}\cdot\left(\sqrt{5}+1\right)}{\sqrt{2}\left(\sqrt{5}+1\right)}=\dfrac{\sqrt{5}}{\sqrt{2}}=\dfrac{\sqrt{10}}{2}\)
\(d.\)
\(\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\dfrac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
\(=\dfrac{\sqrt{5}\cdot\left(\sqrt{3}-1\right)}{\sqrt{3}-1}+\dfrac{\sqrt{5}\left(\sqrt{5}-2\right)}{2\cdot\left(\sqrt{5}-2\right)}\)
\(=\sqrt{5}+\dfrac{\sqrt{5}}{2}=\dfrac{3\sqrt{5}}{2}\)
