Question

answer it with steps simplify
$\frac{4 + \sqrt{5} }{4 - \sqrt{5} } + \frac{4 - \sqrt{5} }{4 + \sqrt{5} }$

Answer 1

$\huge {\bold {Solutions:-}}$

$\: \: \: \: \: \: \frac{4 + \sqrt{5} }{4 - \sqrt{5} } + \frac{4 - \sqrt{5} }{4 + \sqrt{5} } \\ = \frac{4 + \sqrt{5} }{4 - \sqrt{5} } \times \frac{4 + \sqrt{5} }{4 + \sqrt{5} } \\ \: \: \: \: \: \: \: \: \: \: \: + \frac{4 - \sqrt{5} }{4 + \sqrt{5} } \times \frac{4 - \sqrt{5} }{4 - \sqrt{5} } \\ = \frac{ {(4)}^{2} + { (\sqrt{5}) }^{2} }{ {(4)}^{2} - {( \sqrt{5} )}^{2} } + \frac{ {(4)}^{2} + {( \sqrt{5}) }^{2} }{ {(4)}^{2} - {( \sqrt{5} )}^{2} } \\ = \frac{16 + 5}{16 - 5} + \frac{16 + 5}{16 - 5} \\ = \frac{21}{11} + \frac{21}{11} \\ = \frac{42}{11}$
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