Whakaoti i te frac{1+sqrt{15}}{1-sqrt{15}}

$$\frac{ 1+ \sqrt{ 15 } }{ 1- \sqrt{ 15 } }$$

Aromātai

$$\frac{-\sqrt{15}-8}{7}\approx -1.696140478$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{1+\sqrt{15}}{1-\sqrt{15}} mā te whakarea i te taurunga me te tauraro ki te 1+\sqrt{15}.

$$\frac{\left(1+\sqrt{15}\right)\left(1+\sqrt{15}\right)}{\left(1-\sqrt{15}\right)\left(1+\sqrt{15}\right)}$$

Whakaarohia te \left(1-\sqrt{15}\right)\left(1+\sqrt{15}\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}.

$$\frac{\left(1+\sqrt{15}\right)\left(1+\sqrt{15}\right)}{1^{2}-\left(\sqrt{15}\right)^{2}}$$

Pūrua 1. Pūrua \sqrt{15}.

$$\frac{\left(1+\sqrt{15}\right)\left(1+\sqrt{15}\right)}{1-15}$$

Tangohia te 15 i te 1, ka -14.

$$\frac{\left(1+\sqrt{15}\right)\left(1+\sqrt{15}\right)}{-14}$$

Whakareatia te 1+\sqrt{15} ki te 1+\sqrt{15}, ka \left(1+\sqrt{15}\right)^{2}.

$$\frac{\left(1+\sqrt{15}\right)^{2}}{-14}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(1+\sqrt{15}\right)^{2}.

$$\frac{1+2\sqrt{15}+\left(\sqrt{15}\right)^{2}}{-14}$$

Ko te pūrua o \sqrt{15} ko 15.

$$\frac{1+2\sqrt{15}+15}{-14}$$

Tāpirihia te 1 ki te 15, ka 16.

$$\frac{16+2\sqrt{15}}{-14}$$