Question

3+√6 DIVIDIDO POR 5√3-5√2

Answer 1

$\frac{3+ \sqrt{6}}{5 \sqrt{3}-5 \sqrt{2}} = \\\\ \frac{(3+ \sqrt{6})*(5 \sqrt{3}+5 \sqrt{2})}{(5 \sqrt{3}-5 \sqrt{2})(5 \sqrt{3}+5 \sqrt{2})} = \\\\ \frac{15 \sqrt{3} + 15 \sqrt{2} + 15 \sqrt{2} + 10 \sqrt{3} }{(5 \sqrt{3} )^{2} - (5 \sqrt{2} )^{2}} = \\\\ \boxed{\boxed{\sqrt{3} + \frac{6 \sqrt{2} }{5}}}$ 

Answer 2

Olá Leonardo,

A resolução por ser a seguinte:

$\frac{3+\sqrt{6}}{5\sqrt{3}-5\sqrt{2}}={\frac{3+\sqrt{6}}{5\sqrt{3}-5\sqrt{2}}\cdot{\frac{5\sqrt{3}+5\sqrt{2}}{5\sqrt{3}+5\sqrt{2}}$
$\frac{3+\sqrt{6}}{5\sqrt{3}-5\sqrt{2}}={\frac{5(3+\sqrt{6})(\sqrt{3}+\sqrt{2})}{25}$
$\frac{3+\sqrt{6}}{5\sqrt{3}-5\sqrt{2}}={\frac{5\sqrt{3}+6\sqrt{2}}{5}$
$\frac{3+\sqrt{6}}{5\sqrt{3}-5\sqrt{2}}=\sqrt{3}+{\frac{6\sqrt{2}}{5}$

Abraço,

Douglas Joziel.