\(\dfrac{3\sqrt{7}+7\sqrt{3}}{\sqrt{21}}=\dfrac{\sqrt{21}\left(\sqrt{3}+\sqrt{7}\right)}{\sqrt{21}}=\sqrt{3}+\sqrt{7}\)
\(\dfrac{2\sqrt{5}-4\sqrt{10}}{3\sqrt{10}}=\dfrac{\sqrt{10}\left(\sqrt{2}-4\right)}{3\sqrt{10}}=\dfrac{\sqrt{2}-4}{3}\)
\(\dfrac{a-\sqrt{a}}{\sqrt{a}-1}=\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}=\sqrt{a}\)