Whakaoti i te 1/x-3-1x-3

$$\frac { 1 } { x - 3 } - 1 x - 3$$

Aromātai

$$\frac{10-x^{2}}{x-3}$$

Ngā Hipanga Rongoā Poto

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

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

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

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

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

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

Whakakotahitia ngā kupu rite i 1-x^{2}+3x-3x+9.

$$\frac{10-x^{2}}{x-3}$$

Kimi Pārōnaki e ai ki x

$$\frac{-x^{2}+6x-10}{\left(x-3\right)^{2}}$$

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 -x-3 ki te \frac{x-3}{x-3}.

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

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

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

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

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

Whakakotahitia ngā kupu rite i 1-x^{2}+3x-3x+9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10-x^{2}}{x-3})$$

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.

$$\frac{\left(x^{1}-3\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+10)-\left(-x^{2}+10\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-3)}{\left(x^{1}-3\right)^{2}}$$

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}.

$$\frac{\left(x^{1}-3\right)\times 2\left(-1\right)x^{2-1}-\left(-x^{2}+10\right)x^{1-1}}{\left(x^{1}-3\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(x^{1}-3\right)\left(-2\right)x^{1}-\left(-x^{2}+10\right)x^{0}}{\left(x^{1}-3\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{x^{1}\left(-2\right)x^{1}-3\left(-2\right)x^{1}-\left(-x^{2}x^{0}+10x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

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

$$\frac{-2x^{1+1}-3\left(-2\right)x^{1}-\left(-x^{2}+10x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{-2x^{2}+6x^{1}-\left(-x^{2}+10x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{-2x^{2}+6x^{1}-\left(-x^{2}\right)-10x^{0}}{\left(x^{1}-3\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(-2-\left(-1\right)\right)x^{2}+6x^{1}-10x^{0}}{\left(x^{1}-3\right)^{2}}$$

Tango -1 mai i -2.

$$\frac{-x^{2}+6x^{1}-10x^{0}}{\left(x^{1}-3\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-x^{2}+6x-10x^{0}}{\left(x-3\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-x^{2}+6x-10\times 1}{\left(x-3\right)^{2}}$$

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

$$\frac{-x^{2}+6x-10}{\left(x-3\right)^{2}}$$