Question

What is the following quotient? StartFraction 1 Over 1 + StartRoot 3 EndRoot EndFraction StartFraction StartRoot 3 EndRoot Over 4 EndFraction StartFraction 1 + StartRoot 3 EndRoot Over 4 EndFraction StartFraction 1 minus StartRoot 3 EndRoot Over 4 EndFraction StartFraction negative 1 + StartRoot 3 EndRoot Over 2 EndFraction

Answer 1

D

Explanation:

edge2020

Answer 2

D. StartFraction negative 1 + StartRoot 3 EndRoot Over 2 EndFraction

Explanation:

Multiply numerator and denominator by the conjugate of the denominator. Then the denominator is the difference of squares, which will be rational. This simplification is called "rationalizing the denominator."

`(1)/(1+√(3))=(1)/(1+√(3))\cdot(1-√(3))/(1-√(3))=(1-√(3))/(1^2-(√(3))^2)\\\\=(1-√(3))/(-2)=\boxed{(-1+√(3))/(2)}`