Whakaoti i te frac{1/sqrt{2}-1/sqrt{3}}{1-1/sqrt{6}}

$$\frac { \frac { 1 } { \sqrt { 2 } } - \frac { 1 } { \sqrt { 3 } } } { 1 - \frac { 1 } { \sqrt { 6 } } }$$

Aromātai

$$\frac{2\sqrt{2}-\sqrt{3}}{5}\approx 0.219275263$$

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}.

$$\frac{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{1}{\sqrt{3}}}{1-\frac{1}{\sqrt{6}}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\frac{\sqrt{2}}{2}-\frac{1}{\sqrt{3}}}{1-\frac{1}{\sqrt{6}}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{1-\frac{1}{\sqrt{6}}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{3}}{1-\frac{1}{\sqrt{6}}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2 me 3 ko 6. Whakareatia \frac{\sqrt{2}}{2} ki te \frac{3}{3}. Whakareatia \frac{\sqrt{3}}{3} ki te \frac{2}{2}.

$$\frac{\frac{3\sqrt{2}}{6}-\frac{2\sqrt{3}}{6}}{1-\frac{1}{\sqrt{6}}}$$

Tā te mea he rite te tauraro o \frac{3\sqrt{2}}{6} me \frac{2\sqrt{3}}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{1-\frac{1}{\sqrt{6}}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{1-\frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{1-\frac{\sqrt{6}}{6}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{6}{6}.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{\frac{6}{6}-\frac{\sqrt{6}}{6}}$$

Tā te mea he rite te tauraro o \frac{6}{6} me \frac{\sqrt{6}}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{\frac{6-\sqrt{6}}{6}}$$

Whakawehe \frac{3\sqrt{2}-2\sqrt{3}}{6} ki te \frac{6-\sqrt{6}}{6} mā te whakarea \frac{3\sqrt{2}-2\sqrt{3}}{6} ki te tau huripoki o \frac{6-\sqrt{6}}{6}.

$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\times 6}{6\left(6-\sqrt{6}\right)}$$

Me whakakore tahi te 6 i te taurunga me te tauraro.

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

Whakangāwaritia te tauraro o \frac{-2\sqrt{3}+3\sqrt{2}}{-\sqrt{6}+6} mā te whakarea i te taurunga me te tauraro ki te -\sqrt{6}-6.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{\left(-\sqrt{6}+6\right)\left(-\sqrt{6}-6\right)}$$

Whakaarohia te \left(-\sqrt{6}+6\right)\left(-\sqrt{6}-6\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}.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{\left(-\sqrt{6}\right)^{2}-6^{2}}$$

Whakarohaina te \left(-\sqrt{6}\right)^{2}.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{\left(-1\right)^{2}\left(\sqrt{6}\right)^{2}-6^{2}}$$

Tātaihia te -1 mā te pū o 2, kia riro ko 1.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{1\left(\sqrt{6}\right)^{2}-6^{2}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{1\times 6-6^{2}}$$

Whakareatia te 1 ki te 6, ka 6.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{6-6^{2}}$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{6-36}$$

Tangohia te 36 i te 6, ka -30.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{-30}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o -2\sqrt{3}+3\sqrt{2} ki ia tau o -\sqrt{6}-6.

$$\frac{2\sqrt{3}\sqrt{6}+12\sqrt{3}-3\sqrt{2}\sqrt{6}-18\sqrt{2}}{-30}$$

Tauwehea te 6=3\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3\times 2} hei hua o ngā pūtake rua \sqrt{3}\sqrt{2}.

$$\frac{2\sqrt{3}\sqrt{3}\sqrt{2}+12\sqrt{3}-3\sqrt{2}\sqrt{6}-18\sqrt{2}}{-30}$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$\frac{2\times 3\sqrt{2}+12\sqrt{3}-3\sqrt{2}\sqrt{6}-18\sqrt{2}}{-30}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{6\sqrt{2}+12\sqrt{3}-3\sqrt{2}\sqrt{6}-18\sqrt{2}}{-30}$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

$$\frac{6\sqrt{2}+12\sqrt{3}-3\sqrt{2}\sqrt{2}\sqrt{3}-18\sqrt{2}}{-30}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$\frac{6\sqrt{2}+12\sqrt{3}-3\times 2\sqrt{3}-18\sqrt{2}}{-30}$$

Whakareatia te -3 ki te 2, ka -6.

$$\frac{6\sqrt{2}+12\sqrt{3}-6\sqrt{3}-18\sqrt{2}}{-30}$$

Pahekotia te 12\sqrt{3} me -6\sqrt{3}, ka 6\sqrt{3}.

$$\frac{6\sqrt{2}+6\sqrt{3}-18\sqrt{2}}{-30}$$

Pahekotia te 6\sqrt{2} me -18\sqrt{2}, ka -12\sqrt{2}.

$$\frac{-12\sqrt{2}+6\sqrt{3}}{-30}$$