Whakaoti i te 5/-5-3sqrt{3}

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

Aromātai

$$\frac{25-15\sqrt{3}}{2}\approx -0.490381057$$

Ngā Upane Otinga

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

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

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

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

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

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

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

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

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

$$\frac{5\left(-5+3\sqrt{3}\right)}{25-9\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{5\left(-5+3\sqrt{3}\right)}{25-9\times 3}$$

Whakareatia te 9 ki te 3, ka 27.

$$\frac{5\left(-5+3\sqrt{3}\right)}{25-27}$$

Tangohia te 27 i te 25, ka -2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te -5+3\sqrt{3}.

$$\frac{-25+15\sqrt{3}}{-2}$$