Question

ALGUEM AÍ MANJA ME EXPLICAR?
$\frac{1}{1- \sqrt[2]{2} } - \frac{1}{ \sqrt[2]{2} +1}$

VLW!!

Answer 1

$\dfrac{1}{1-\sqrt{2}}=\dfrac{1\cdot(1+\sqrt{2})}{(1-\sqrt{2})(1+\sqrt{2})}=\dfrac{1+\sqrt{2}}{1-2}=-1-\sqrt{2}$

$\dfrac{1}{1+\sqrt{2}}=\dfrac{1\cdot(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}=\dfrac{\sqrt{2}-1}{2-1}=\sqrt{2}-1$

Logo:

$\dfrac{1}{1-\sqrt{2}}-\dfrac{1}{\sqrt{2}+1}=-1-\sqrt{2}-\sqrt{2}+1=-2\sqrt{2}$