Simplify \((\frac{1}{\sqrt{5} + \sqrt{3}} - \frac{1}{\sqrt{5} - \sqrt{3}}) \times \frac{1}{\sqrt{3}}\)
\((\frac{1}{\sqrt{5} + \sqrt{3}} - \frac{1}{\sqrt{5} - \sqrt{3}}) \times \frac{1}{\sqrt{3}}\)
\(\frac{1}{\sqrt{5} + \sqrt{3}} - \frac{1}{\sqrt{5} - \sqrt{3}}\)
\(\frac{(\sqrt{5} - \sqrt{3}) - (\sqrt{5} + \sqrt{3})}{(\sqrt{5} + \sqrt{3})(\sqrt{5} - \sqrt{3})}\)
= \(\frac{\sqrt{5} - \sqrt{3} - \sqrt{5} - \sqrt{3}}{5 - \sqrt{15} + \sqrt{15} - 3}\)
= \(\frac{-2\sqrt{3}}{2}\)
= \(- \sqrt{3}\)
\(\therefore (\frac{1}{\sqrt{5} + \sqrt{3}} - \frac{1}{\sqrt{5} - \sqrt{3}}) \times \frac{1}{\sqrt{3}} = - \sqrt{3} \times \frac{1}{\sqrt{3}}\)
= \(-1\)
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