Whakaoti i te 1/2-sqrt{3}+1/2+sqrt{3}+frac{sqrt{8}}{sqrt{2}}

$$\frac { 1 } { 2 - \sqrt { 3 } } + \frac { 1 } { 2 + \sqrt { 3 } } + \frac { \sqrt { 8 } } { \sqrt { 2 } }$$

Aromātai

$$6$$

Ngā Upane Otinga

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

$$\frac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

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

$$\frac{2+\sqrt{3}}{2^{2}-\left(\sqrt{3}\right)^{2}}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

Pūrua 2. Pūrua \sqrt{3}.

$$\frac{2+\sqrt{3}}{4-3}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

Tangohia te 3 i te 4, ka 1.

$$\frac{2+\sqrt{3}}{1}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$2+\sqrt{3}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

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

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

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

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

Pūrua 2. Pūrua \sqrt{3}.

$$2+\sqrt{3}+\frac{2-\sqrt{3}}{4-3}+\frac{\sqrt{8}}{\sqrt{2}}$$

Tangohia te 3 i te 4, ka 1.

$$2+\sqrt{3}+\frac{2-\sqrt{3}}{1}+\frac{\sqrt{8}}{\sqrt{2}}$$

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

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

Tāpirihia te 2 ki te 2, ka 4.

$$4+\sqrt{3}-\sqrt{3}+\frac{\sqrt{8}}{\sqrt{2}}$$

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

$$4+\frac{\sqrt{8}}{\sqrt{2}}$$

Tuhia anō te whakawehe o ngā pūtake rua \frac{\sqrt{8}}{\sqrt{2}} hei pūtake rua o te whakawehenga \sqrt{\frac{8}{2}} ka mahi i te whakawehenga.

$$4+\sqrt{4}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$4+2$$

Tāpirihia te 4 ki te 2, ka 6.

$$6$$

Tauwehe

$$2\times 3$$