Simplify \(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) - \(\frac{3 - 2}{\sqrt{3} + \sqrt{2}}\)

A.

2\(\sqrt{2} - \sqrt{3}\)

B.

3(\(\sqrt{6}\) - 1)

C.

\(\sqrt{6}\) - 3

D.

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

E.

\(\frac{-\sqrt{3}}{\sqrt{2} - \sqrt{2}}\)

Correct answer is B

\(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) - \(\frac{3 - 2}{\sqrt{3} + \sqrt{2}}\)

\(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) = \(\frac{\sqrt{2}}{\sqrt{3}}\) - \(\frac{x}{\sqrt{2}}\)

\(\frac{\sqrt{3} + \sqrt{2}}{3 + \sqrt{2}}\) = \(\sqrt{6}\) + 2

\(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) = \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) x \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}\)

= 5 - 2\(\sqrt{6}\)

\(\sqrt{6}\) + 2 - (5 - 2 \(\sqrt{6}\)) = \(\sqrt{6}\) + 2 - 5 + 2\(\sqrt{6}\)

= 3\(\sqrt{6}\) - 3

= 3(\(\sqrt{6}\) - 1)