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\frac{6\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}
Rationalize the denominator of \frac{6}{2\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.
\frac{6\sqrt{7}}{2\times 7}
The square of \sqrt{7} is 7.
\frac{3\sqrt{7}}{7}
Cancel out 2 in both numerator and denominator.