Question

Rationalize the denominator of the fraction and enter the new denominator below.

8/2-√12

Answer 1

`(8)/(2-√(12))\\ (8(2+√(12)))/(4-12)=\\ (8(2+√(12)))/(-8)=\\ -(2+√(12)})=\\ -2-√(12)=\\-2-2\sqrt3`

Answer 2

`(8)/(2-√(12))=(8)/(2-√(4\cdot3))=(8)/(2-2\sqrt3)=(8)/(2(1-\sqrt3))=(4)/(1-\sqrt3)\\\\(4)/(1-\sqrt3)\cdot(1+\sqrt3)/(1+\sqrt3)=(4(1+\sqrt3))/(1^2-(\sqrt3)^2)=(4(1+\sqrt3))/(1-3)=(4(1+\sqrt3))/(-2)=-2(1+\sqrt3)}\\\\=-2-2\sqrt3`




`if\ (8)/(2)-√(12)=4-√(4\cdot3)=4-2\sqrt3`