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\frac{-2}{2\left(-\sqrt{3}\right)}
Divide \frac{-1}{2} by \frac{-\sqrt{3}}{2} by multiplying \frac{-1}{2} by the reciprocal of \frac{-\sqrt{3}}{2}.
\frac{-1}{-\sqrt{3}}
Cancel out 2 in both numerator and denominator.
\frac{-\sqrt{3}}{-\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{-1}{-\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
\frac{-\sqrt{3}}{-3}
The square of \sqrt{3} is 3.
\frac{\sqrt{3}}{3}
Cancel out -1 in both numerator and denominator.