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\frac{\left(\sqrt{3}-\sqrt{7}\right)\left(\sqrt{3}-\sqrt{7}\right)}{\left(\sqrt{3}+\sqrt{7}\right)\left(\sqrt{3}-\sqrt{7}\right)}
Whakangāwaritia te tauraro o \frac{\sqrt{3}-\sqrt{7}}{\sqrt{3}+\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}-\sqrt{7}.
\frac{\left(\sqrt{3}-\sqrt{7}\right)\left(\sqrt{3}-\sqrt{7}\right)}{\left(\sqrt{3}\right)^{2}-\left(\sqrt{7}\right)^{2}}
Whakaarohia te \left(\sqrt{3}+\sqrt{7}\right)\left(\sqrt{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{\left(\sqrt{3}-\sqrt{7}\right)\left(\sqrt{3}-\sqrt{7}\right)}{3-7}
Pūrua \sqrt{3}. Pūrua \sqrt{7}.
\frac{\left(\sqrt{3}-\sqrt{7}\right)\left(\sqrt{3}-\sqrt{7}\right)}{-4}
Tangohia te 7 i te 3, ka -4.
\frac{\left(\sqrt{3}-\sqrt{7}\right)^{2}}{-4}
Whakareatia te \sqrt{3}-\sqrt{7} ki te \sqrt{3}-\sqrt{7}, ka \left(\sqrt{3}-\sqrt{7}\right)^{2}.
\frac{\left(\sqrt{3}\right)^{2}-2\sqrt{3}\sqrt{7}+\left(\sqrt{7}\right)^{2}}{-4}
Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{3}-\sqrt{7}\right)^{2}.
\frac{3-2\sqrt{3}\sqrt{7}+\left(\sqrt{7}\right)^{2}}{-4}
Ko te pūrua o \sqrt{3} ko 3.
\frac{3-2\sqrt{21}+\left(\sqrt{7}\right)^{2}}{-4}
Hei whakarea \sqrt{3} me \sqrt{7}, whakareatia ngā tau i raro i te pūtake rua.
\frac{3-2\sqrt{21}+7}{-4}
Ko te pūrua o \sqrt{7} ko 7.
\frac{10-2\sqrt{21}}{-4}
Tāpirihia te 3 ki te 7, ka 10.