Question

Simplify:
$\frac{1}{5 + \sqrt{7} }$
​

Answer 1

Answer:

$\frac{1}{5 + \sqrt{7} } \times \frac{5 - \sqrt{7} }{5 - \sqrt{7} } \\ \\ = \frac{5 - \sqrt{7} }{ {5}^{2} - { \sqrt{7} }^{2} } \\ \\ = \frac{5 - \sqrt{7} }{25 - 7} \\ \\ = \frac{5 - \sqrt{7} }{18}$