Question

simplify 7−2√5/7+2√5 + 7+2√5/7-2√5

Answer 1

Answer:

$\frac{138}{29}$

Step-by-step explanation:

$\frac{7 - 2 \sqrt{5} }{7 + 2 \sqrt{5} } + \frac{7 + 2 \sqrt{5} }{7 - 2 \sqrt{5} }$

$\frac{ {(7 - 2 \sqrt{5} )}^{2} + {(7 + 2 \sqrt{5}) }^{2} }{(7 + 2 \sqrt{5} )(7 - 2 \sqrt{5}) }$

$\frac{49 + 20 - 28 \sqrt{5} + 49 + 20 + 28 \sqrt{5} }{ {7}^{2} - {(2 \sqrt{5}) }^{2} }$

$\frac{138}{49 - 20}$

$\frac{138}{29}$