Question

5+√3÷5-√3+5- √3÷ 5+√3​

Answer 1

Step-by-step explanation:

$5 + \sqrt{3} \div 5 - \sqrt{3} + 5 - \sqrt{3} \div 5 + \sqrt{3}$

$= \frac{5 + \sqrt{3} }{5 - \sqrt{3} } + \frac{5 - \sqrt{3} }{5 + \sqrt{3} }$

$= \frac{( {5 + \sqrt{3} )}^{2} + ( {5 - \sqrt{3}) }^{2} }{(5 - \sqrt{3})(5 + \sqrt{3}) }$

$= \frac{ ({5})^{2} + 2 \times 5 \times \sqrt{3} + ( { \sqrt{3}) }^{2} + ( {5)}^{2} - 2 \times 5 \times \sqrt{3} + ( { \sqrt{3} })^{2} }{( {5})^{2} - ( { \sqrt{3}) }^{2} }$

$= \frac{25 + 10 \sqrt{3} + 3 + 25 - 10 \sqrt{3} + 3 }{25 - 3}$

$= \frac{56}{22}$

$= \frac{28}{11}$