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: B
Explanation
\(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) - \(\frac{3 - 2}{\sqrt{3} + \sqrt{2}}\)
\(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) = \(\frac{\sqrt{2}}{\sqrt{3}}\) - \(\frac{x}{\sqrt{2}}\)
\(\frac{\sqrt{3} + \sqrt{2}}{3 + \sqrt{2}}\) = \(\sqrt{6}\) + 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)
