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

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

A.

3\(\sqrt{6} - 7\)

B.

3\(\sqrt{6} + 7\)

C.

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

D.

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

Correct answer is A

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

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

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

\(= \frac{4 - 3\sqrt{6} + 3}{-1}\)

\(= \frac{7 - 3\sqrt{6}}{-1}\)

\(= \frac{7}{-1} - \frac{3\sqrt{6}}{-1}\)

\(= -7 + 3\sqrt{6}\)

\(= 3\sqrt{6}-7\)