Question on: JAMB Mathematics - 2014
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\(\sqrt{6} + 1\)
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Correct Option: 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)
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