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

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

Aromātai

$$-2$$

Ngā Hipanga Rongoā Poto

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

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

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

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

Pūrua -2. Pūrua \sqrt{2}.

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

Tangohia te 2 i te 4, ka 2.

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

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

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

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

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

Pūrua -2. Pūrua \sqrt{2}.

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

Tangohia te 2 i te 4, ka 2.

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

Tā te mea he rite te tauraro o \frac{-2+\sqrt{2}}{2} me \frac{-2-\sqrt{2}}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Mahia ngā tātaitai i roto o -2+\sqrt{2}-2-\sqrt{2}.

$$\frac{-4}{2}$$

Whakawehea te -4 ki te 2, kia riro ko -2.

$$-2$$

Tauwehe

$$-2$$