\(\dfrac{1}{\sqrt{5}-\sqrt[]{3}}-\dfrac{1}{\sqrt{5}+\sqrt{3}}\)
\(=\dfrac{\sqrt{5}+\sqrt{3}-\sqrt{5}+\sqrt{3}}{5-3}\)
\(=\dfrac{2\sqrt{3}}{2}=\sqrt{3}\)
\[
(\sqrt{5} - \sqrt{3})(\sqrt{5} + \sqrt{3})
\]
\[
a^2 - b^2 = (\sqrt{5})^2 - (\sqrt{3})^2 = 5 - 3 = 2
\]
\[
\frac{1}{\sqrt{5} - \sqrt{3}} = \frac{\sqrt{5} + \sqrt{3}}{(\sqrt{5} - \sqrt{3})(\sqrt{5} + \sqrt{3})} = \frac{\sqrt{5} + \sqrt{3}}{2}
\]
\[
\frac{1}{\sqrt{5} + \sqrt{3}} = \frac{\sqrt{5} - \sqrt{3}}{(\sqrt{5} + \sqrt{3})(\sqrt{5} - \sqrt{3})} = \frac{\sqrt{5} - \sqrt{3}}{2}
\]
\[
\frac{\sqrt{5} + \sqrt{3}}{2} - \frac{\sqrt{5} - \sqrt{3}}{2}
\]
\[
= \frac{(\sqrt{5} + \sqrt{3}) - (\sqrt{5} - \sqrt{3})}{2}
\]
\[
= \frac{\sqrt{5} + \sqrt{3} - \sqrt{5} + \sqrt{3}}{2}
\]
\[
= \frac{2\sqrt{3}}{2} = \sqrt{3}
\]
