Rationalize \(\frac{2 - \sqrt5}{3 - \sqrt5}\)

A.

\(\frac{1 - \sqrt5}{2}\)

B.

\(\frac{1 - \sqrt5}{4}\)

C.

\(\frac{ \sqrt5 - 1}{2}\)

D.

\(\frac{1 + \sqrt5}{4}\)

Correct answer is B

\(\frac{2 - \sqrt5}{3 - \sqrt5}\) x \(\frac{3 + \sqrt5}{3 + \sqrt5}\)

\(\frac{(2 - \sqrt5)(3 + \sqrt5)}{(3 - \sqrt5)(3 + \sqrt5)}\) = \(\frac{6 +2\sqrt5 - 3\sqrt5 - \sqrt25}{9 + 3\sqrt5 - 3\sqrt5 - \sqrt25}\)

= \(\frac{6 - \sqrt5 - 5}{9 - 5}\)

= \(\frac{1 - \sqrt5}{4}\)