Whakaoti i te 2xdiv3x^3/x-4

$$2 x \div \frac { 3 x ^ { 3 } } { x - 4 }$$

Aromātai

$$\frac{2\left(x-4\right)}{3x^{2}}$$

Ngā Hipanga Rongoā Poto

Whakawehe 2x ki te \frac{3x^{3}}{x-4} mā te whakarea 2x ki te tau huripoki o \frac{3x^{3}}{x-4}.

$$\frac{2x\left(x-4\right)}{3x^{3}}$$

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

$$\frac{2\left(x-4\right)}{3x^{2}}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x-4.

$$\frac{2x-8}{3x^{2}}$$

Kimi Pārōnaki e ai ki x

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

Ngā Upane e Whakamahi ana i te Ture Pārōnaki mō te Otinga

Whakawehe 2x ki te \frac{3x^{3}}{x-4} mā te whakarea 2x ki te tau huripoki o \frac{3x^{3}}{x-4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\left(x-4\right)}{3x^{3}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x-4\right)}{3x^{2}})$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x-4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-8}{3x^{2}})$$

Mō ngā pānga e rua e taea ana te pārōnaki, ko te pārōnaki o te otinga o ngā pānga e rua ko te tauraro whakareatia ki te pārōnaki o te taurunga tango i te taurunga whakareatia ki te pārōnaki o te tauraro, ā, ka whakawehea te katoa ki te tauraro kua pūruatia.

$$\frac{3x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}-8)-\left(2x^{1}-8\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2})}{\left(3x^{2}\right)^{2}}$$

Ko te pārōnaki o tētahi pūrau ko te tapeke o ngā pārōnaki o ōna kīanga tau. Ko te pārōnaki o tētahi kīanga tau pūmau ko 0. Ko te pārōnaki o te ax^{n} ko te nax^{n-1}.

$$\frac{3x^{2}\times 2x^{1-1}-\left(2x^{1}-8\right)\times 2\times 3x^{2-1}}{\left(3x^{2}\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{3x^{2}\times 2x^{0}-\left(2x^{1}-8\right)\times 6x^{1}}{\left(3x^{2}\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{3x^{2}\times 2x^{0}-\left(2x^{1}\times 6x^{1}-8\times 6x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

Hei whakarea pū o te pūtake ōrite, tāpiri ana taupū.

$$\frac{3\times 2x^{2}-\left(2\times 6x^{1+1}-8\times 6x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{6x^{2}-\left(12x^{2}-48x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{6x^{2}-12x^{2}-\left(-48x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(6-12\right)x^{2}-\left(-48x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

Tango 12 mai i 6.

$$\frac{-6x^{2}-\left(-48x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

Tauwehea te 6x.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{\left(3x^{2}\right)^{2}}$$

Hei hiki i te hua o ngā tau e rua, neke atu rānei ki tētahi pū, hīkina ia tau ki te pū ka tuhi ko tāna hua.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{3^{2}\left(x^{2}\right)^{2}}$$

Hīkina te 3 ki te pū 2.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{9\left(x^{2}\right)^{2}}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{9x^{2\times 2}}$$

Whakareatia 2 ki te 2.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{9x^{4}}$$

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te taurunga i te taupū o te tauraro.

$$\frac{6\left(-x^{1}-\left(-8x^{0}\right)\right)}{9x^{4-1}}$$

Tango 1 mai i 4.

$$\frac{6\left(-x^{1}-\left(-8x^{0}\right)\right)}{9x^{3}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{6\left(-x-\left(-8x^{0}\right)\right)}{9x^{3}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{6\left(-x-\left(-8\right)\right)}{9x^{3}}$$