Rationalize \(\frac{2 – \sqrt5}{3 – \sqrt5}\)
- \(\frac{1 - \sqrt5}{2}\)
-
\(\frac{1 - \sqrt5}{4}\)
- \(\frac{ \sqrt5 - 1}{2}\)
- \(\frac{1 + \sqrt5}{4}\)
The correct answer is: B
Explanation
\(\frac{2 - \sqrt5}{3 - \sqrt5}\) x \(\frac{3 + \sqrt5}{3 + \sqrt5}\)\(\frac{(2 - \sqrt5)(3 + \sqrt5)}{(3 - \sqrt5)(3 + \sqrt5)}\) = \(\frac{6 +2\sqrt5 - 3\sqrt5 - \sqrt25}{9 + 3\sqrt5 - 3\sqrt5 - \sqrt25}\)
= \(\frac{6 - \sqrt5 - 5}{9 - 5}\)
= \(\frac{1 - \sqrt5}{4}\)
There is an explanation video available .