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\frac{\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{1}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
\frac{\sqrt{3}}{2\times 3}
The square of \sqrt{3} is 3.
\frac{\sqrt{3}}{6}
Multiply 2 and 3 to get 6.