Whakaoti i te frac{sqrt{6}}{sqrt{2}tsqrt{3}}=frac{sqrt{6}(sqrt{2}-sqrt{3})}{(sqrt{2}+sqrt{3})(sqrt{2}-sqrt{3})}=

$$\frac { \sqrt { 6 } } { \sqrt { 2 } t \sqrt { 3 } } = \frac { \sqrt { 6 } ( \sqrt { 2 } - \sqrt { 3 } ) } { ( \sqrt { 2 } + \sqrt { 3 } ) ( \sqrt { 2 } - \sqrt { 3 } ) } =$$

Whakaoti mō t

$$t = \frac{2 \sqrt{3} + 3 \sqrt{2}}{6} \approx 1.28445705$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

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

Ko te pūrua o \sqrt{6} ko 6.

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

Whakareatia te \sqrt{6} ki te \sqrt{6}, ka 6.

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

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}.

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

Pūrua \sqrt{2}. Pūrua \sqrt{3}.

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

Tangohia te 3 i te 2, ka -1.

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{6} ki te \sqrt{2}-\sqrt{3}.

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

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}.

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

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

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

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}.

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

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

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

Hei kimi i te tauaro o 2\sqrt{3}-3\sqrt{2}, kimihia te tauaro o ia taurangi.

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

Tē taea kia ōrite te tāupe t ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 6t.

$$6=-2\sqrt{3}\times 6t+3\sqrt{2}\times 6t$$

Whakaraupapatia anō ngā kīanga tau.

$$6=3\times 6\sqrt{2}t-2\times 6\sqrt{3}t$$

Mahia ngā whakarea.

$$6=18\sqrt{2}t-12\sqrt{3}t$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$18\sqrt{2}t-12\sqrt{3}t=6$$

Pahekotia ngā kīanga tau katoa e whai ana i te t.

$$\left(18\sqrt{2}-12\sqrt{3}\right)t=6$$

Whakawehea ngā taha e rua ki te 18\sqrt{2}-12\sqrt{3}.

$$\frac{\left(18\sqrt{2}-12\sqrt{3}\right)t}{18\sqrt{2}-12\sqrt{3}}=\frac{6}{18\sqrt{2}-12\sqrt{3}}$$

Mā te whakawehe ki te 18\sqrt{2}-12\sqrt{3} ka wetekia te whakareanga ki te 18\sqrt{2}-12\sqrt{3}.

$$t=\frac{6}{18\sqrt{2}-12\sqrt{3}}$$

Whakawehe 6 ki te 18\sqrt{2}-12\sqrt{3}.

$$t=\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}$$