Whakaoti i te frac{3/2+sqrt{3}-2/2-sqrt{3}}{2-5sqrt{3}}

$$\frac { \frac { 3 } { 2 + \sqrt { 3 } } - \frac { 2 } { 2 - \sqrt { 3 } } } { 2 - 5 \sqrt { 3 } }$$

Aromātai

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Ngā Upane Otinga

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

$$\frac{\frac{3\left(2-\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

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

$$\frac{\frac{3\left(2-\sqrt{3}\right)}{2^{2}-\left(\sqrt{3}\right)^{2}}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

Pūrua 2. Pūrua \sqrt{3}.

$$\frac{\frac{3\left(2-\sqrt{3}\right)}{4-3}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

Tangohia te 3 i te 4, ka 1.

$$\frac{\frac{3\left(2-\sqrt{3}\right)}{1}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

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

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2\left(2+\sqrt{3}\right)}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}}{2-5\sqrt{3}}$$

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

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2\left(2+\sqrt{3}\right)}{2^{2}-\left(\sqrt{3}\right)^{2}}}{2-5\sqrt{3}}$$

Pūrua 2. Pūrua \sqrt{3}.

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2\left(2+\sqrt{3}\right)}{4-3}}{2-5\sqrt{3}}$$

Tangohia te 3 i te 4, ka 1.

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2\left(2+\sqrt{3}\right)}{1}}{2-5\sqrt{3}}$$

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$\frac{3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)}{2-5\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)}{2-5\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 2+5\sqrt{3}.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{\left(2-5\sqrt{3}\right)\left(2+5\sqrt{3}\right)}$$

Whakaarohia te \left(2-5\sqrt{3}\right)\left(2+5\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}.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{2^{2}-\left(-5\sqrt{3}\right)^{2}}$$

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

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-\left(-5\sqrt{3}\right)^{2}}$$

Whakarohaina te \left(-5\sqrt{3}\right)^{2}.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-\left(-5\right)^{2}\left(\sqrt{3}\right)^{2}}$$

Tātaihia te -5 mā te pū o 2, kia riro ko 25.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-25\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-25\times 3}$$

Whakareatia te 25 ki te 3, ka 75.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-75}$$

Tangohia te 75 i te 4, ka -71.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{-71}$$

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

$$\frac{\left(6-3\sqrt{3}-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{-71}$$

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

$$\frac{\left(6-3\sqrt{3}-\left(4+2\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{-71}$$

Hei kimi i te tauaro o 4+2\sqrt{3}, kimihia te tauaro o ia taurangi.

$$\frac{\left(6-3\sqrt{3}-4-2\sqrt{3}\right)\left(2+5\sqrt{3}\right)}{-71}$$

Tangohia te 4 i te 6, ka 2.

$$\frac{\left(2-3\sqrt{3}-2\sqrt{3}\right)\left(2+5\sqrt{3}\right)}{-71}$$

Pahekotia te -3\sqrt{3} me -2\sqrt{3}, ka -5\sqrt{3}.

$$\frac{\left(2-5\sqrt{3}\right)\left(2+5\sqrt{3}\right)}{-71}$$

Whakaarohia te \left(2-5\sqrt{3}\right)\left(2+5\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}.

$$\frac{2^{2}-\left(5\sqrt{3}\right)^{2}}{-71}$$

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

$$\frac{4-\left(5\sqrt{3}\right)^{2}}{-71}$$

Whakarohaina te \left(5\sqrt{3}\right)^{2}.

$$\frac{4-5^{2}\left(\sqrt{3}\right)^{2}}{-71}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\frac{4-25\left(\sqrt{3}\right)^{2}}{-71}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{4-25\times 3}{-71}$$

Whakareatia te 25 ki te 3, ka 75.

$$\frac{4-75}{-71}$$

Tangohia te 75 i te 4, ka -71.

$$\frac{-71}{-71}$$

Whakawehea te -71 ki te -71, kia riro ko 1.

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Tauwehe

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