Question

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Answer 1

$\displaystyle \frac{5}{\sqrt{13}+\sqrt{3}} = \frac{5}{\sqrt{13}+\sqrt{3}} \cdot \frac{\sqrt{13}-\sqrt{3}}{\sqrt{13}-\sqrt{3}} = \\\\\\ \displaystyle \frac{5(\sqrt{13}-\sqrt{3})}{13-3} = \frac{5(\sqrt{13}-\sqrt{3})}{10} = \frac{\sqrt{13}-\sqrt{3}}{2}$