Whakaoti i te 2/3+sqrt{-5}:3

$$\frac { 2 } { 3 + \sqrt { - 5 } } : 3$$

Aromātai

$$\text{Indeterminate}$$

Ngā Upane Otinga

Tuhia te \frac{\frac{2}{3+\sqrt{-5}}}{3} hei hautanga kotahi.

$$\frac{2}{\left(3+\sqrt{-5}\right)\times 3}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3+\sqrt{-5} ki te 3.

$$\frac{2}{9+3\sqrt{-5}}$$

Whakangāwaritia te tauraro o \frac{2}{9+3\sqrt{-5}} mā te whakarea i te taurunga me te tauraro ki te 9-3\sqrt{-5}.

$$\frac{2\left(9-3\sqrt{-5}\right)}{\left(9+3\sqrt{-5}\right)\left(9-3\sqrt{-5}\right)}$$

Whakaarohia te \left(9+3\sqrt{-5}\right)\left(9-3\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}.

$$\frac{2\left(9-3\sqrt{-5}\right)}{9^{2}-\left(3\sqrt{-5}\right)^{2}}$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$\frac{2\left(9-3\sqrt{-5}\right)}{81-\left(3\sqrt{-5}\right)^{2}}$$

Whakarohaina te \left(3\sqrt{-5}\right)^{2}.

$$\frac{2\left(9-3\sqrt{-5}\right)}{81-3^{2}\left(\sqrt{-5}\right)^{2}}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$\frac{2\left(9-3\sqrt{-5}\right)}{81-9\left(\sqrt{-5}\right)^{2}}$$

Tātaihia te \sqrt{-5} mā te pū o 2, kia riro ko -5.

$$\frac{2\left(9-3\sqrt{-5}\right)}{81-9\left(-5\right)}$$

Whakareatia te 9 ki te -5, ka -45.

$$\frac{2\left(9-3\sqrt{-5}\right)}{81-\left(-45\right)}$$

Whakareatia te -1 ki te -45, ka 45.

$$\frac{2\left(9-3\sqrt{-5}\right)}{81+45}$$

Tāpirihia te 81 ki te 45, ka 126.

$$\frac{2\left(9-3\sqrt{-5}\right)}{126}$$

Whakawehea te 2\left(9-3\sqrt{-5}\right) ki te 126, kia riro ko \frac{1}{63}\left(9-3\sqrt{-5}\right).

$$\frac{1}{63}\left(9-3\sqrt{-5}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{63} ki te 9-3\sqrt{-5}.

$$\frac{1}{63}\times 9+\frac{1}{63}\left(-3\right)\sqrt{-5}$$

Whakareatia te \frac{1}{63} ki te 9, ka \frac{9}{63}.

$$\frac{9}{63}+\frac{1}{63}\left(-3\right)\sqrt{-5}$$

Whakahekea te hautanga \frac{9}{63} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$\frac{1}{7}+\frac{1}{63}\left(-3\right)\sqrt{-5}$$

Whakareatia te \frac{1}{63} ki te -3, ka \frac{-3}{63}.

$$\frac{1}{7}+\frac{-3}{63}\sqrt{-5}$$

Whakahekea te hautanga \frac{-3}{63} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{1}{7}-\frac{1}{21}\sqrt{-5}$$