Whakaoti i te frac{sqrt{2}-2sqrt{3}}{sqrt{2}-sqrt{3}}

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

Aromātai

$$\sqrt{6}+4\approx 6.449489743$$

Ngā Upane Otinga

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

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

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

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

Pūrua \sqrt{2}. Pūrua \sqrt{3}.

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

Tangohia te 3 i te 2, ka -1.

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

Ko te mea whakawehea ki te -1 ka hōmai i tōna kōaro.

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

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

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

Ko te pūrua o \sqrt{2} ko 2.

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

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

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

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

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

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

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

Tangohia te 6 i te 2, ka -4.

$$-\left(-4-\sqrt{6}\right)$$

Hei kimi i te tauaro o -4-\sqrt{6}, kimihia te tauaro o ia taurangi.

$$-\left(-4\right)-\left(-\sqrt{6}\right)$$

Ko te tauaro o -4 ko 4.

$$4-\left(-\sqrt{6}\right)$$

Ko te tauaro o -\sqrt{6} ko \sqrt{6}.

$$4+\sqrt{6}$$