Mathematics: Rationalize the denominator of the fraction and enter the new denominator below.8/2-√12

Rationalize the denominator of the fraction and enter

Ответ:

CelesteN64

31.12.2021

$\frac{8}{2-\sqrt{12}}=\frac{8}{2-\sqrt{4\cdot3}}=\frac{8}{2-2\sqrt3}=\frac{8}{2(1-\sqrt3)}=\frac{4}{1-\sqrt3}\\\\\frac{4}{1-\sqrt3}\cdot\frac{1+\sqrt3}{1+\sqrt3}=\frac{4(1+\sqrt3)}{1^2-(\sqrt3)^2}=\frac{4(1+\sqrt3)}{1-3}=\frac{4(1+\sqrt3)}{-2}=-2(1+\sqrt3)}\\\\=-2-2\sqrt3$

$if\ \frac{8}{2}-\sqrt{12}=4-\sqrt{4\cdot3}=4-2\sqrt3$