Whakaoti i te 3x+2+1/3x+2

$$3 x + 2 + \frac { 1 } { 3 x + 2 }$$

Aromātai

$$\frac{9x^{2}+12x+5}{3x+2}$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 3x+2 ki te \frac{3x+2}{3x+2}.

$$\frac{\left(3x+2\right)\left(3x+2\right)}{3x+2}+\frac{1}{3x+2}$$

Tā te mea he rite te tauraro o \frac{\left(3x+2\right)\left(3x+2\right)}{3x+2} me \frac{1}{3x+2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\left(3x+2\right)\left(3x+2\right)+1}{3x+2}$$

Mahia ngā whakarea i roto o \left(3x+2\right)\left(3x+2\right)+1.

$$\frac{9x^{2}+6x+6x+4+1}{3x+2}$$

Whakakotahitia ngā kupu rite i 9x^{2}+6x+6x+4+1.

$$\frac{9x^{2}+12x+5}{3x+2}$$

Kimi Pārōnaki e ai ki x

$$\frac{9\left(x+1\right)\left(3x+1\right)}{\left(3x+2\right)^{2}}$$

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 3x+2 ki te \frac{3x+2}{3x+2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(3x+2\right)\left(3x+2\right)}{3x+2}+\frac{1}{3x+2})$$

Tā te mea he rite te tauraro o \frac{\left(3x+2\right)\left(3x+2\right)}{3x+2} me \frac{1}{3x+2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(3x+2\right)\left(3x+2\right)+1}{3x+2})$$

Mahia ngā whakarea i roto o \left(3x+2\right)\left(3x+2\right)+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9x^{2}+6x+6x+4+1}{3x+2})$$

Whakakotahitia ngā kupu rite i 9x^{2}+6x+6x+4+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9x^{2}+12x+5}{3x+2})$$

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.

$$\frac{\left(3x^{1}+2\right)\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2}+12x^{1}+5)-\left(9x^{2}+12x^{1}+5\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1}+2)}{\left(3x^{1}+2\right)^{2}}$$

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}.

$$\frac{\left(3x^{1}+2\right)\left(2\times 9x^{2-1}+12x^{1-1}\right)-\left(9x^{2}+12x^{1}+5\right)\times 3x^{1-1}}{\left(3x^{1}+2\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(3x^{1}+2\right)\left(18x^{1}+12x^{0}\right)-\left(9x^{2}+12x^{1}+5\right)\times 3x^{0}}{\left(3x^{1}+2\right)^{2}}$$

Whakareatia 3x^{1}+2 ki te 18x^{1}+12x^{0}.

$$\frac{3x^{1}\times 18x^{1}+3x^{1}\times 12x^{0}+2\times 18x^{1}+2\times 12x^{0}-\left(9x^{2}+12x^{1}+5\right)\times 3x^{0}}{\left(3x^{1}+2\right)^{2}}$$

Whakareatia 9x^{2}+12x^{1}+5 ki te 3x^{0}.

$$\frac{3x^{1}\times 18x^{1}+3x^{1}\times 12x^{0}+2\times 18x^{1}+2\times 12x^{0}-\left(9x^{2}\times 3x^{0}+12x^{1}\times 3x^{0}+5\times 3x^{0}\right)}{\left(3x^{1}+2\right)^{2}}$$

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

$$\frac{3\times 18x^{1+1}+3\times 12x^{1}+2\times 18x^{1}+2\times 12x^{0}-\left(9\times 3x^{2}+12\times 3x^{1}+5\times 3x^{0}\right)}{\left(3x^{1}+2\right)^{2}}$$

Whakarūnātia.

$$\frac{54x^{2}+36x^{1}+36x^{1}+24x^{0}-\left(27x^{2}+36x^{1}+15x^{0}\right)}{\left(3x^{1}+2\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{27x^{2}+36x^{1}+9x^{0}}{\left(3x^{1}+2\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{27x^{2}+36x+9x^{0}}{\left(3x+2\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{27x^{2}+36x+9\times 1}{\left(3x+2\right)^{2}}$$

Mō tētahi kupu t, t\times 1=t me 1t=t.

$$\frac{27x^{2}+36x+9}{\left(3x+2\right)^{2}}$$