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
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
= \(\frac{1 - \sqrt{5} - 1 - \sqrt{5}}{(1 + \sqrt{5}) (1 - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{1 - 5}\)
= \(\frac{-2\sqrt{5}}{- 4}\)
= \(\frac{1}{2}\sqrt{5}\)
Source: Myschool Past Questions Archive (Record #31378)