Question

desculpem, errei o enunciado. O correto é: 1 sobre 3 + rais quadrada de 8 (tudo isso menos o inverso, ou seja: ) 1 sobre 3 - rais quadrada de 8.
Achei que primeiro deveria aplicar a propriedade distributiva, mas já me enrolei todo...

Answer 1

Resposta:

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

Explicação passo-a-passo:

$\frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}} = \frac{1\cdot(3-\sqrt{3})}{3+\sqrt{3}\cdot(3-\sqrt{3})} - \frac{1\cdot(3+\sqrt{3})}{3-\sqrt{3}\cdot(3+\sqrt{3})}\\\\\frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}} = \frac{3-\sqrt{3}}{3^2-\sqrt{3}^2} -\frac{3+\sqrt{3}}{3^2-\sqrt{3}^2}\\\\\frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}} = \frac{3-\sqrt{3}}{9-3} -\frac{3+\sqrt{3}}{9-3}\\\\\frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}} = \frac{3-\sqrt{3}}{6} -\frac{3+\sqrt{3}}{6}$

$\frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}} = \frac{(3-\sqrt{3})-(3+\sqrt{3})}{6}\\\\\frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}} = \frac{3-\sqrt{3}-3-\sqrt{3}}{6}\\\\\frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}} = \frac{-2\sqrt{3}}{6}\\\\\frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}} = \frac{-\sqrt{3}}{3}\\\\\frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}} = -\frac{\sqrt{3}}{3}$