Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
\(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\) = \(\frac{1 - \sqrt{5} - 1 - \sqrt{5}}{(1 + \sqrt{5}) (1 - \sqrt{5}}\) = \(\frac{-2\sqrt{5}}{1 - 5}\) = \(\frac{-2\sqrt{5}}{- 4}\) = \(\frac{1}{2}\sqrt{5}\)
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