Question on: JAMB Mathematics - 2009
Simplify (\frac{5+\sqrt{7}}{3+\sqrt{7}})
A
17-√7
B
4-√7
C
15+√7
D
7-√7
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Correct Option: B
(\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\
=\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\
=\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\
=\frac{8-2\sqrt{7}}{2})
Factorize then divide by 2
(=\frac{2(4-\sqrt{7}}{2}\
=4-\sqrt{7})
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