a) \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}=\dfrac{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}{\sqrt{2}.\sqrt{2}}=\dfrac{\sqrt{10}-\sqrt{6}}{2}\)
b) \(\dfrac{a-2\sqrt{a}}{\sqrt{a}-2}=\dfrac{\left(\sqrt{a}+2\right)\sqrt{a}\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}=\dfrac{\sqrt{a}\left(a-4\right)}{a-4}=\sqrt{a}\)
c) \(\dfrac{13}{2\sqrt{3}-5}=\dfrac{13\left(2\sqrt{3}+5\right)}{\left(2\sqrt{3}-5\right)\left(2\sqrt{3}+5\right)}=\dfrac{13\left(2\sqrt{3}+5\right)}{12-25}=\dfrac{13\left(2\sqrt{3}+5\right)}{-13}=-5-2\sqrt{3}\)
2d/
\(\frac{2\sqrt{10}-5}{4-\sqrt{10}}=\frac{\sqrt{5}(2\sqrt{2}-\sqrt{5})}{\sqrt{2}(2\sqrt{2}-\sqrt{5})}=\frac{\sqrt{5}}{\sqrt{2}}=\frac{\sqrt{10}}{2}\)
