Whakaoti i te frac{sqrt{7}+sqrt{5}}{sqrt{7}-sqrt{5}}-sqrt{35}

$$\frac{ \sqrt{ 7 } + \sqrt{ 5 } }{ \sqrt{ 7 } - \sqrt{ 5 } } - \sqrt{ 35 }$$

Aromātai

$$6$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{7}+\sqrt{5}.

$$\frac{\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}{\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}-\sqrt{35}$$

Whakaarohia te \left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\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}.

$$\frac{\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}{\left(\sqrt{7}\right)^{2}-\left(\sqrt{5}\right)^{2}}-\sqrt{35}$$

Pūrua \sqrt{7}. Pūrua \sqrt{5}.

$$\frac{\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}{7-5}-\sqrt{35}$$

Tangohia te 5 i te 7, ka 2.

$$\frac{\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}{2}-\sqrt{35}$$

Whakareatia te \sqrt{7}+\sqrt{5} ki te \sqrt{7}+\sqrt{5}, ka \left(\sqrt{7}+\sqrt{5}\right)^{2}.

$$\frac{\left(\sqrt{7}+\sqrt{5}\right)^{2}}{2}-\sqrt{35}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{7}+\sqrt{5}\right)^{2}.

$$\frac{\left(\sqrt{7}\right)^{2}+2\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^{2}}{2}-\sqrt{35}$$

Ko te pūrua o \sqrt{7} ko 7.

$$\frac{7+2\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^{2}}{2}-\sqrt{35}$$

Hei whakarea \sqrt{7} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{7+2\sqrt{35}+\left(\sqrt{5}\right)^{2}}{2}-\sqrt{35}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{7+2\sqrt{35}+5}{2}-\sqrt{35}$$

Tāpirihia te 7 ki te 5, ka 12.

$$\frac{12+2\sqrt{35}}{2}-\sqrt{35}$$

Whakawehea ia wā o 12+2\sqrt{35} ki te 2, kia riro ko 6+\sqrt{35}.

$$6+\sqrt{35}-\sqrt{35}$$

Pahekotia te \sqrt{35} me -\sqrt{35}, ka 0.

$$6$$

Tauwehe

$$2\times 3$$