Question

simplify : -
$\frac{2}{5 + \sqrt{3} } - \frac{2}{5 - \sqrt{3} }$
​

Answer 1

$\underline{\underline{\sf \color{Orchid}{Question}}} : \sf \dfrac{2}{5 + \sqrt{3} } - \dfrac{2}{5 - \sqrt{3} }$

$\underline{\underline{\sf \color{Orchid}{Answer}}} :$

$\sf \dfrac{2}{5 + \sqrt{3} } - \dfrac{2}{5 - \sqrt{3} }$

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

$\sf \: = \dfrac{10 - 2 \sqrt{3} - 10 - 2 \sqrt{ 3} }{25 - 3}$

$\sf \: = \dfrac{ - 4 \sqrt{3} }{22}$

$\sf \: = \dfrac{ - 2 \sqrt{3} }{11}$

$\\ \boxed{ \boxed{ \sf \dfrac{2}{5 + \sqrt{3} } - \dfrac{2}{5 - \sqrt{3} } = \dfrac{ - 2 \sqrt{3} }{11} }}$