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\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Whakangāwaritia te tauraro o \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}+\sqrt{3}.
\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Whakaarohia te \left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\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{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{5-3}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Pūrua \sqrt{5}. Pūrua \sqrt{3}.
\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Tangohia te 3 i te 5, ka 2.
\frac{\left(\sqrt{5}+\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Whakareatia te \sqrt{5}+\sqrt{3} ki te \sqrt{5}+\sqrt{3}, ka \left(\sqrt{5}+\sqrt{3}\right)^{2}.
\frac{\left(\sqrt{5}\right)^{2}+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{5}+\sqrt{3}\right)^{2}.
\frac{5+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Ko te pūrua o \sqrt{5} ko 5.
\frac{5+2\sqrt{15}+\left(\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Hei whakarea \sqrt{5} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.
\frac{5+2\sqrt{15}+3}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Ko te pūrua o \sqrt{3} ko 3.
\frac{8+2\sqrt{15}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Tāpirihia te 5 ki te 3, ka 8.
4+\sqrt{15}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
Whakawehea ia wā o 8+2\sqrt{15} ki te 2, kia riro ko 4+\sqrt{15}.
4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}
Whakangāwaritia te tauraro o \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}-\sqrt{3}.
4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}
Whakaarohia te \left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\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}.
4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{5-3}
Pūrua \sqrt{5}. Pūrua \sqrt{3}.
4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{2}
Tangohia te 3 i te 5, ka 2.
4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)^{2}}{2}
Whakareatia te \sqrt{5}-\sqrt{3} ki te \sqrt{5}-\sqrt{3}, ka \left(\sqrt{5}-\sqrt{3}\right)^{2}.
4+\sqrt{15}+\frac{\left(\sqrt{5}\right)^{2}-2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}
Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{5}-\sqrt{3}\right)^{2}.
4+\sqrt{15}+\frac{5-2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}
Ko te pūrua o \sqrt{5} ko 5.
4+\sqrt{15}+\frac{5-2\sqrt{15}+\left(\sqrt{3}\right)^{2}}{2}
Hei whakarea \sqrt{5} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.
4+\sqrt{15}+\frac{5-2\sqrt{15}+3}{2}
Ko te pūrua o \sqrt{3} ko 3.
4+\sqrt{15}+\frac{8-2\sqrt{15}}{2}
Tāpirihia te 5 ki te 3, ka 8.
4+\sqrt{15}+4-\sqrt{15}
Whakawehea ia wā o 8-2\sqrt{15} ki te 2, kia riro ko 4-\sqrt{15}.
8+\sqrt{15}-\sqrt{15}
Tāpirihia te 4 ki te 4, ka 8.
8
Pahekotia te \sqrt{15} me -\sqrt{15}, ka 0.