a) \(\dfrac{8}{\sqrt{2}}=\dfrac{8\sqrt{2}}{2}=4\sqrt{2}\)
b) \(\dfrac{15}{4\sqrt{3}}=\dfrac{15\sqrt{3}}{12}=\dfrac{5\sqrt{3}}{4}\)
c) \(\dfrac{5}{\sqrt{5}+1}=\dfrac{5\left(\sqrt{5}-1\right)}{5-1}=\dfrac{5\sqrt{5}-5}{4}\)
d) \(\dfrac{5-\sqrt{5}}{\sqrt{5}-1}=\dfrac{\sqrt{5}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}=\sqrt{5}\)