Whakaoti i te frac{2+sqrt{3}}{3sqrt{2}+2sqrt{7}}

$$\frac { 2 + \sqrt { 3 } } { 3 \sqrt { 2 } + 2 \sqrt { 7 } }$$

Aromātai

$$\frac{\sqrt{21}}{5}+\frac{2\sqrt{7}}{5}-\frac{3\sqrt{2}}{5}-\frac{3\sqrt{6}}{10}\approx 0.391440603$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{2+\sqrt{3}}{3\sqrt{2}+2\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te 3\sqrt{2}-2\sqrt{7}.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{\left(3\sqrt{2}+2\sqrt{7}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}$$

Whakaarohia te \left(3\sqrt{2}+2\sqrt{7}\right)\left(3\sqrt{2}-2\sqrt{7}\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}.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{7}\right)^{2}}$$

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

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{3^{2}\left(\sqrt{2}\right)^{2}-\left(2\sqrt{7}\right)^{2}}$$

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

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{9\left(\sqrt{2}\right)^{2}-\left(2\sqrt{7}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{9\times 2-\left(2\sqrt{7}\right)^{2}}$$

Whakareatia te 9 ki te 2, ka 18.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-\left(2\sqrt{7}\right)^{2}}$$

Whakarohaina te \left(2\sqrt{7}\right)^{2}.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-2^{2}\left(\sqrt{7}\right)^{2}}$$

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

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-4\left(\sqrt{7}\right)^{2}}$$

Ko te pūrua o \sqrt{7} ko 7.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-4\times 7}$$

Whakareatia te 4 ki te 7, ka 28.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-28}$$

Tangohia te 28 i te 18, ka -10.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{-10}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2+\sqrt{3} ki ia tau o 3\sqrt{2}-2\sqrt{7}.

$$\frac{6\sqrt{2}-4\sqrt{7}+3\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{7}}{-10}$$

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

$$\frac{6\sqrt{2}-4\sqrt{7}+3\sqrt{6}-2\sqrt{3}\sqrt{7}}{-10}$$

Hei whakarea \sqrt{3} me \sqrt{7}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{6\sqrt{2}-4\sqrt{7}+3\sqrt{6}-2\sqrt{21}}{-10}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-6\sqrt{2}+4\sqrt{7}-3\sqrt{6}+2\sqrt{21}}{10}$$