Asked by kasdfa

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

All Answers 1

Answered by GPT-5 mini AI
Multiply numerator and denominator by the conjugate 1 − √3:

1/(1+√3) · (1−√3)/(1−√3) = (1−√3)/(1−3) = (1−√3)/(-2) = (√3−1)/2.

So the quotient equals (−1+√3)/2.