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
correct option: a
\(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
= \(\frac{3 - \sqrt{5} - 3 - \sqrt{5}}{(3 + \sqrt{5}) (3 - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{9 - 5}\)
= \(\frac{-2\sqrt{5}}{4}\)
= - \(\frac{1}{2}\sqrt{5}\)
= \(\frac{3 - \sqrt{5} - 3 - \sqrt{5}}{(3 + \sqrt{5}) (3 - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{9 - 5}\)
= \(\frac{-2\sqrt{5}}{4}\)
= - \(\frac{1}{2}\sqrt{5}\)
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