Whakaoti i te 12/3+sqrt{3}-8+2sqrt{3}

$$\frac { 12 } { 3 + \sqrt { 3 } } - 8 + 2 \sqrt { 3 }$$

Aromātai

$$-2$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{12}{3+\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 3-\sqrt{3}.

$$\frac{12\left(3-\sqrt{3}\right)}{\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)}-8+2\sqrt{3}$$

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

$$\frac{12\left(3-\sqrt{3}\right)}{3^{2}-\left(\sqrt{3}\right)^{2}}-8+2\sqrt{3}$$

Pūrua 3. Pūrua \sqrt{3}.

$$\frac{12\left(3-\sqrt{3}\right)}{9-3}-8+2\sqrt{3}$$

Tangohia te 3 i te 9, ka 6.

$$\frac{12\left(3-\sqrt{3}\right)}{6}-8+2\sqrt{3}$$

Whakawehea te 12\left(3-\sqrt{3}\right) ki te 6, kia riro ko 2\left(3-\sqrt{3}\right).

$$2\left(3-\sqrt{3}\right)-8+2\sqrt{3}$$

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

$$6-2\sqrt{3}-8+2\sqrt{3}$$

Tangohia te 8 i te 6, ka -2.

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

Pahekotia te -2\sqrt{3} me 2\sqrt{3}, ka 0.

$$-2$$

Tauwehe

$$-2$$