Question

Simplifique (raízes):

Answer 1

$\frac{2 + \sqrt{3} }{ 2\sqrt{2}+ \sqrt{3} } + \frac{ 2 - \sqrt{3} }{ \sqrt{2} - \sqrt{2}- \sqrt{3} }$

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

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

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

Agora a distributiva...

$\frac{4\sqrt{2}-2\sqrt{3}+ 2\sqrt{6}-3}{5} - \frac{ 2\sqrt{3}-3 }{ 3}$

Colocar na mesma fração

$\frac{(4\sqrt{2}-2\sqrt{3}+ 2\sqrt{6}-3)(3)}{(5)(3)} - \frac{ (2\sqrt{3}-3)(5) }{ (3)(5)}$


$\frac{(4\sqrt{2}-2\sqrt{3}+ 2\sqrt{6}-3)3 -(2\sqrt{3}-3)5}{15}$

$\frac{12\sqrt{2}-6\sqrt{3}+ 6\sqrt{6}-9 -(10\sqrt{3}-15)}{15}$

$\frac{12\sqrt{2}-6\sqrt{3}+ 6\sqrt{6}-9 -10\sqrt{3}+15)}{15}$

É esta é a conclusão

$\frac{12\sqrt{2}-16\sqrt{3}+ 6\sqrt{6}+6}{15}$