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

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

Aromātai

$$-6\sqrt{3}-10\approx -20.392304845$$

Ngā Upane Otinga

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

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

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}.

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

Pūrua \sqrt{3}. Pūrua 2.

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

Tangohia te 4 i te 3, ka -1.

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

Ko te mea whakawehea ki te -1 ka hōmai i tōna kōaro.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2+2\sqrt{3} ki ia tau o \sqrt{3}+2.

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

Ko te pūrua o \sqrt{3} ko 3.

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

Whakareatia te 2 ki te 3, ka 6.

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

Tāpirihia te 4 ki te 6, ka 10.

$$-\left(2\sqrt{3}+10+4\sqrt{3}\right)$$

Pahekotia te 2\sqrt{3} me 4\sqrt{3}, ka 6\sqrt{3}.

$$-\left(6\sqrt{3}+10\right)$$

Hei kimi i te tauaro o 6\sqrt{3}+10, kimihia te tauaro o ia taurangi.

$$-6\sqrt{3}-10$$

Tauwehe

$$2 {(-3 \sqrt{3} - 5)} = -20.392304845$$