Correct Answer: Option B

Explanation

\(\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\)
=\(\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\)
=\(\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\)
= \(\frac{8-2\sqrt{7}}{2}\)
Factorize, then divide by 2
\(=\frac{2(4-\sqrt{7}}{2})\)
=4-\(\sqrt{7}\)

There is an explanation video available below.

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