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

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

Aromātai

$$\sqrt{3}-2\approx -0.267949192$$

Ngā Upane Otinga

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

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

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

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

Pūrua \sqrt{3}. Pūrua 3.

$$\frac{\left(\sqrt{3}-3\right)\left(\sqrt{3}-3\right)}{3-9}$$

Tangohia te 9 i te 3, ka -6.

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

Whakareatia te \sqrt{3}-3 ki te \sqrt{3}-3, ka \left(\sqrt{3}-3\right)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{3}-3\right)^{2}.

$$\frac{\left(\sqrt{3}\right)^{2}-6\sqrt{3}+9}{-6}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{3-6\sqrt{3}+9}{-6}$$

Tāpirihia te 3 ki te 9, ka 12.

$$\frac{12-6\sqrt{3}}{-6}$$

Whakawehea ia wā o 12-6\sqrt{3} ki te -6, kia riro ko -2+\sqrt{3}.

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