Whakaoti i te frac{sqrt{14}+2}{1-sqrt{7}}

$$\frac{ \sqrt{ 14 } +2 }{ 1- \sqrt{ 7 } }$$

Aromātai

$$-\frac{\sqrt{7}}{3}-\frac{\sqrt{14}}{6}-\frac{7\sqrt{2}}{6}-\frac{1}{3}\approx -3.488775824$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{\sqrt{14}+2}{1-\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te 1+\sqrt{7}.

$$\frac{\left(\sqrt{14}+2\right)\left(1+\sqrt{7}\right)}{\left(1-\sqrt{7}\right)\left(1+\sqrt{7}\right)}$$

Whakaarohia te \left(1-\sqrt{7}\right)\left(1+\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}.

$$\frac{\left(\sqrt{14}+2\right)\left(1+\sqrt{7}\right)}{1^{2}-\left(\sqrt{7}\right)^{2}}$$

Pūrua 1. Pūrua \sqrt{7}.

$$\frac{\left(\sqrt{14}+2\right)\left(1+\sqrt{7}\right)}{1-7}$$

Tangohia te 7 i te 1, ka -6.

$$\frac{\left(\sqrt{14}+2\right)\left(1+\sqrt{7}\right)}{-6}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o \sqrt{14}+2 ki ia tau o 1+\sqrt{7}.

$$\frac{\sqrt{14}+\sqrt{14}\sqrt{7}+2+2\sqrt{7}}{-6}$$

Tauwehea te 14=7\times 2. Tuhia anō te pūtake rua o te hua \sqrt{7\times 2} hei hua o ngā pūtake rua \sqrt{7}\sqrt{2}.

$$\frac{\sqrt{14}+\sqrt{7}\sqrt{2}\sqrt{7}+2+2\sqrt{7}}{-6}$$

Whakareatia te \sqrt{7} ki te \sqrt{7}, ka 7.

$$\frac{\sqrt{14}+7\sqrt{2}+2+2\sqrt{7}}{-6}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-\sqrt{14}-7\sqrt{2}-2-2\sqrt{7}}{6}$$