Whakaoti i te frac{sqrt{4}abc+sqrt{10}a^{2}b^{3}c^5-sqrt{6}a^3b^2c^6}{sqrt{2}abc}

$$\frac { \sqrt { 4 } a b c + \sqrt { 10 } a ^ { 2 } b ^ { 3 } c ^ { 5 } - \sqrt { 6 } a ^ { 3 } b ^ { 2 } c ^ { 6 } } { \sqrt { 2 } a b c }$$

Tauwehe

$$\frac{\sqrt{2}\left(-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2\right)}{2}$$

Ngā Upane Otinga

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$factor(\frac{2abc+\sqrt{10}a^{2}b^{3}c^{5}-\sqrt{6}a^{3}b^{2}c^{6}}{\sqrt{2}abc})$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{2abc+\sqrt{10}a^{2}b^{3}c^{5}-\sqrt{6}a^{3}b^{2}c^{6}}{\sqrt{2}abc}.

$$factor(\frac{abc\left(-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2\right)}{\sqrt{2}abc})$$

Me whakakore tahi te abc i te taurunga me te tauraro.

$$factor(\frac{-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2}{\sqrt{2}})$$

Whakangāwaritia te tauraro o \frac{-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$factor(\frac{\left(-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}})$$

Ko te pūrua o \sqrt{2} ko 2.

$$factor(\frac{\left(-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2\right)\sqrt{2}}{2})$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2 ki te \sqrt{2}.

$$factor(\frac{-\sqrt{6}ba^{2}c^{5}\sqrt{2}+\sqrt{10}ab^{2}c^{4}\sqrt{2}+2\sqrt{2}}{2})$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

$$factor(\frac{-\sqrt{2}\sqrt{3}ba^{2}c^{5}\sqrt{2}+\sqrt{10}ab^{2}c^{4}\sqrt{2}+2\sqrt{2}}{2})$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$factor(\frac{-2ba^{2}c^{5}\sqrt{3}+\sqrt{10}ab^{2}c^{4}\sqrt{2}+2\sqrt{2}}{2})$$

Tauwehea te 10=2\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2\times 5} hei hua o ngā pūtake rua \sqrt{2}\sqrt{5}.

$$factor(\frac{-2ba^{2}c^{5}\sqrt{3}+\sqrt{2}\sqrt{5}ab^{2}c^{4}\sqrt{2}+2\sqrt{2}}{2})$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$factor(\frac{-2ba^{2}c^{5}\sqrt{3}+2ab^{2}c^{4}\sqrt{5}+2\sqrt{2}}{2})$$

Whakaarohia te -2ba^{2}c^{5}\times 3^{\frac{1}{2}}+2ab^{2}c^{4}\times 5^{\frac{1}{2}}+2\times 2^{\frac{1}{2}}. Tauwehea te 2.

$$2\left(-ba^{2}c^{5}\sqrt{3}+ab^{2}c^{4}\sqrt{5}+\sqrt{2}\right)$$

Me tuhi anō te kīanga whakatauwehe katoa. Whakarūnātia.

$$-ba^{2}c^{5}\sqrt{3}+ab^{2}c^{4}\sqrt{5}+\sqrt{2}$$

Aromātai

$$-\frac{2\sqrt{3}ba^{2}c^{5}}{2}+\frac{2\sqrt{5}ab^{2}c^{4}}{2}+\sqrt{2}$$