Question

Racionalizar o denominador da fração:

 

√2 + 2

√2 - 2

Answer 1

$\frac{\sqrt{2}+2}{\sqrt{2}-2}=\\\\\frac{\sqrt{2}+2}{\sqrt{2}-2}\times\frac{\sqrt{2}+2}{\sqrt{2}+2}=\\\\\frac{\left(\sqrt{2}+2\right)^2}{2-4}=\\\\\frac{2+4\sqrt{2}+4}{-2}=\\\\\frac{6+4\sqrt{2}}{-2}=\\\\\frac{2(3+2\sqrt{2})}{-2}=\\\\\frac{1(3+2\sqrt{2})}{-1}=\\\\\boxed{-3-2\sqrt{2}}$