Simplify frac 1 1 sqrt 5 - frac 1 1 - sqrt 5 - JAMB Mathematics 1991 Question
Simplify (\frac{1}{1 + \sqrt{5}}) - (\frac{1}{1 - \sqrt{5}})
A
- \(\frac{1}{2}\sqrt{5}\)
B
\(\frac{1}{2}\sqrt{5}\)
C
-- \(\frac{1}{4}\sqrt{5}\)
D
5
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Correct Option: A
(\frac{1}{1 + \sqrt{5}}) - (\frac{1}{1 - \sqrt{5}})
= (\frac{3 - \sqrt{5} - 3 - \sqrt{5}}{(3 + \sqrt{5}) (3 - \sqrt{5}})
= (\frac{-2\sqrt{5}}{9 - 5})
= (\frac{-2\sqrt{5}}{4})
= - (\frac{1}{2}\sqrt{5})
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