Simplify \(\frac{2\sqrt{2} – \sqrt{3}}{\sqrt{2} + \sqrt{3}}\)
-
3\(\sqrt{6} - 7\)
- 3\(\sqrt{6} + 7\)
- 3\(\sqrt{6} - 1\)
- 3\(\sqrt{6} + 1\)
The correct answer is: A
Explanation
\(= \frac{2\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}} \times \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)
\(= \frac{2\sqrt{2}(\sqrt{2}) + (2\sqrt{2})(-\sqrt{3})-\sqrt{3}(\sqrt{2})-\sqrt{3}(-\sqrt{3})}{(\sqrt{2})^2-(\sqrt{3})^2}\)
\(= \frac{2 \times 2 - 2\sqrt{6} - \sqrt{6} + 3}{2 - 3}\)
\(= \frac{4 - 3\sqrt{6} + 3}{-1}\)
\(= \frac{7 - 3\sqrt{6}}{-1}\)
\(= \frac{7}{-1} - \frac{3\sqrt{6}}{-1}\)
\(= -7 + 3\sqrt{6}\)
\(= 3\sqrt{6}-7\)
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