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\frac{12\sqrt{7}}{9\left(\sqrt{7}\right)^{2}}
Rationalize the denominator of \frac{12}{9\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.
\frac{12\sqrt{7}}{9\times 7}
The square of \sqrt{7} is 7.
\frac{4\sqrt{7}}{3\times 7}
Cancel out 3 in both numerator and denominator.
\frac{4\sqrt{7}}{21}
Multiply 3 and 7 to get 21.