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

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

Aromātai

$$\frac{3\sqrt{2}+3\sqrt{3}-\sqrt{6}-9}{7}\approx -0.287242376$$

Ngā Upane Otinga

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

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

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

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

Pūrua \sqrt{2}. Pūrua 3.

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

Tangohia te 9 i te 2, ka -7.

$$\frac{\left(\sqrt{3}-3\right)\left(\sqrt{2}-3\right)}{-7}$$

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

$$\frac{\sqrt{3}\sqrt{2}-3\sqrt{3}-3\sqrt{2}+9}{-7}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{6}-3\sqrt{3}-3\sqrt{2}+9}{-7}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-\sqrt{6}+3\sqrt{3}+3\sqrt{2}-9}{7}$$