Whakaoti i te sqrt{3}+2-1/sqrt{3+2}

$$\sqrt{ 3 } +2- \frac{ 1 }{ \sqrt{ 3 } +2 }$$

Aromātai

$$2\sqrt{3}\approx 3.464101615$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{1}{\sqrt{3}+2} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}-2.

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

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

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

Pūrua \sqrt{3}. Pūrua 2.

$$\sqrt{3}+2-\frac{\sqrt{3}-2}{3-4}$$

Tangohia te 4 i te 3, ka -1.

$$\sqrt{3}+2-\frac{\sqrt{3}-2}{-1}$$

Ko te mea whakawehea ki te -1 ka hōmai i tōna kōaro. Hei kimi i te tauaro o \sqrt{3}-2, kimihia te tauaro o ia taurangi.

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

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

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

Ko te tauaro o -\sqrt{3} ko \sqrt{3}.

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

Ko te tauaro o -2 ko 2.

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

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

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

Tangohia te 2 i te 2, ka 0.

$$2\sqrt{3}$$