Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
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Correct Answer: Option B
Explanation:
\(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
= \(\frac{1Â - \sqrt{5} - 1Â - \sqrt{5}}{(1 + \sqrt{5}) (1Â - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{1Â - 5}\)
= \(\frac{-2\sqrt{5}}{- 4}\)
= Â \(\frac{1}{2}\sqrt{5}\)
\(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
= \(\frac{1Â - \sqrt{5} - 1Â - \sqrt{5}}{(1 + \sqrt{5}) (1Â - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{1Â - 5}\)
= \(\frac{-2\sqrt{5}}{- 4}\)
= Â \(\frac{1}{2}\sqrt{5}\)