Whakaoti i te frac{1/sqrt{2}-1}{1/sqrt{2}+sqrt{3}}

$$\frac{ \frac{ 1 }{ \sqrt{ 2 } } -1 }{ \frac{ 1 }{ \sqrt{ 2 } } + \sqrt{ 3 } }$$

Aromātai

$$\frac{\sqrt{2}+\sqrt{6}-2\sqrt{3}-1}{5}\approx -0.120079662$$

Ngā Hipanga Rongoā Poto

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

$$\frac{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-1}{\frac{1}{\sqrt{2}}+\sqrt{3}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\frac{\sqrt{2}}{2}-1}{\frac{1}{\sqrt{2}}+\sqrt{3}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{2}{2}.

$$\frac{\frac{\sqrt{2}}{2}-\frac{2}{2}}{\frac{1}{\sqrt{2}}+\sqrt{3}}$$

Tā te mea he rite te tauraro o \frac{\sqrt{2}}{2} me \frac{2}{2}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{\sqrt{2}-2}{2}}{\frac{1}{\sqrt{2}}+\sqrt{3}}$$

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

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

Ko te pūrua o \sqrt{2} ko 2.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia \sqrt{3} ki te \frac{2}{2}.

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

Tā te mea he rite te tauraro o \frac{\sqrt{2}}{2} me \frac{2\sqrt{3}}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Whakawehe \frac{\sqrt{2}-2}{2} ki te \frac{\sqrt{2}+2\sqrt{3}}{2} mā te whakarea \frac{\sqrt{2}-2}{2} ki te tau huripoki o \frac{\sqrt{2}+2\sqrt{3}}{2}.

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

Me whakakore tahi te 2 i te taurunga me te tauraro.

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

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

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

Whakaarohia te \left(\sqrt{2}+2\sqrt{3}\right)\left(\sqrt{2}-2\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}.

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

Ko te pūrua o \sqrt{2} ko 2.

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

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

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{\left(\sqrt{2}-2\right)\left(\sqrt{2}-2\sqrt{3}\right)}{2-4\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\left(\sqrt{2}-2\right)\left(\sqrt{2}-2\sqrt{3}\right)}{2-4\times 3}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{\left(\sqrt{2}-2\right)\left(\sqrt{2}-2\sqrt{3}\right)}{2-12}$$

Tangohia te 12 i te 2, ka -10.

$$\frac{\left(\sqrt{2}-2\right)\left(\sqrt{2}-2\sqrt{3}\right)}{-10}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o \sqrt{2}-2 ki ia tau o \sqrt{2}-2\sqrt{3}.

$$\frac{\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}-2\sqrt{2}+4\sqrt{3}}{-10}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2-2\sqrt{2}\sqrt{3}-2\sqrt{2}+4\sqrt{3}}{-10}$$

Hei whakarea \sqrt{2} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{2-2\sqrt{6}-2\sqrt{2}+4\sqrt{3}}{-10}$$