Resposta:
Explicação passo a passo:
[tex]\displaystyle \frac{(2+\sqrt3)}{(2+\sqrt6)}:\frac{(\sqrt6-2)}{\sqrt3} = \frac{(2+\sqrt3)}{(\sqrt6+2)}\times \frac{(\sqrt3)}{(\sqrt6-2)} = \\\\\\\ \frac{2\times \sqrt3+\sqrt3\times \sqrt3}{(\sqrt6)^2-(2)^2} = \frac{2\sqrt3+\sqrt{3^2}}{\sqrt{6^2}-4} = \frac{2\sqrt3+3}{6-4} =\frac{3+2\sqrt3}{2}[/tex]
Diferença de quadrados: a² - b² = (a + b)(a - b)
