Question

simplify
4+√5/4-√5+4-√5/4+√5​

Answer 1

Answer:

$= \frac{4 + \sqrt{5} }{4 - \sqrt{5} } + \frac{4 - \sqrt{5} }{4 + \sqrt{5} }$

$= \frac{(4 + \sqrt{5} ) {}^{2} + {(4 - \sqrt{5} )}^{2} }{( {4})^{2} - ({ \sqrt{5} )}^{2} }$

$= \frac{16 + 5 + 8 \sqrt{5} + 16 + 5 - 8 \sqrt{5} }{16 - 5}$

$= \frac{42}{11}$

Answer 2

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