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

Answer:

D

Step-by-step explanation:

edge2020

Answer 2

Answer:

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

Step-by-step 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."

  $\dfrac{1}{1+\sqrt{3}}=\dfrac{1}{1+\sqrt{3}}\cdot\dfrac{1-\sqrt{3}}{1-\sqrt{3}}=\dfrac{1-\sqrt{3}}{1^2-(\sqrt{3})^2}\\\\=\dfrac{1-\sqrt{3}}{-2}=\boxed{\dfrac{-1+\sqrt{3}}{2}}$