Home » Past Questions » Mathematics » Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)

Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)


Question

Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)

Options

A) - \(\frac{1}{2}\sqrt{5}\)

B) \(\frac{1}{2}\sqrt{5}\)

C) -- \(\frac{1}{4}\sqrt{5}\)

D) 5

The correct answer is A.

Explanation:

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

More Past Questions:


Dicussion (1)

  • \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
    = \(\frac{3 - \sqrt{5} - 3 - \sqrt{5}}{(3 + \sqrt{5}) (3 - \sqrt{5}}\)
    = \(\frac{-2\sqrt{5}}{9 - 5}\)
    = \(\frac{-2\sqrt{5}}{4}\)
    = - \(\frac{1}{2}\sqrt{5}\)

    Reply
    Like