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\frac{6\left(3-\sqrt{7}\right)}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}
Whakangāwaritia te tauraro o \frac{6}{3+\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te 3-\sqrt{7}.
\frac{6\left(3-\sqrt{7}\right)}{3^{2}-\left(\sqrt{7}\right)^{2}}
Whakaarohia te \left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{6\left(3-\sqrt{7}\right)}{9-7}
Pūrua 3. Pūrua \sqrt{7}.
\frac{6\left(3-\sqrt{7}\right)}{2}
Tangohia te 7 i te 9, ka 2.
3\left(3-\sqrt{7}\right)
Whakawehea te 6\left(3-\sqrt{7}\right) ki te 2, kia riro ko 3\left(3-\sqrt{7}\right).
9-3\sqrt{7}
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3-\sqrt{7}.