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Simplify frac 5 sqrt 7 3 sqrt 7 - JAMB Mathematics 2009 Question

Simplify (\frac{5 + \sqrt{7}}{3 + \sqrt{7}})

A
17 - \(\sqrt{7}\)
B
4 - \(\sqrt{7}\)
C
15 - \(\sqrt{7}\)
D
7 - \(\sqrt{7}\)
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Correct Option: B

(\frac{5 + \sqrt{7}}{3 + \sqrt{7}}) x (\frac{3 + \sqrt{7}}{3 + \sqrt{7}})

(\frac{15 - 5 \sqrt{7} + 3\sqrt{7} - 7}{9 - 3\sqrt{7} + 3\sqrt{7} - 7

= 4 - 2(\sqrt{7})

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