JAMB - Mathematics (1991 - No. 10)
Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
- \(\frac{1}{2}\sqrt{5}\)
\(\frac{1}{2}\sqrt{5}\)
-- \(\frac{1}{4}\sqrt{5}\)
5
Explanation
\(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
= \(\frac{1 - \sqrt{5} - 1 - \sqrt{5}}{(1 + \sqrt{5}) (1 - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{1 - 5}\)
= \(\frac{-2\sqrt{5}}{- 4}\)
= \(\frac{1}{2}\sqrt{5}\)
= \(\frac{1 - \sqrt{5} - 1 - \sqrt{5}}{(1 + \sqrt{5}) (1 - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{1 - 5}\)
= \(\frac{-2\sqrt{5}}{- 4}\)
= \(\frac{1}{2}\sqrt{5}\)
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