Whakaoti i te v/v+1+3/v-1-6/v^2-1

$$\frac { v } { v + 1 } + \frac { 3 } { v - 1 } - \frac { 6 } { v ^ { 2 } - 1 }$$

Aromātai

$$\frac{v+3}{v+1}$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o v+1 me v-1 ko \left(v-1\right)\left(v+1\right). Whakareatia \frac{v}{v+1} ki te \frac{v-1}{v-1}. Whakareatia \frac{3}{v-1} ki te \frac{v+1}{v+1}.

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

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

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

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

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

Whakakotahitia ngā kupu rite i v^{2}-v+3v+3.

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

Tauwehea te v^{2}-1.

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

Tā te mea he rite te tauraro o \frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)} me \frac{6}{\left(v-1\right)\left(v+1\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Whakakotahitia ngā kupu rite i v^{2}+2v+3-6.

$$\frac{v^{2}+2v-3}{\left(v-1\right)\left(v+1\right)}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{v^{2}+2v-3}{\left(v-1\right)\left(v+1\right)}.

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

Me whakakore tahi te v-1 i te taurunga me te tauraro.

$$\frac{v+3}{v+1}$$

Kimi Pārōnaki e ai ki v

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

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. Ko te taurea pātahi iti rawa o v+1 me v-1 ko \left(v-1\right)\left(v+1\right). Whakareatia \frac{v}{v+1} ki te \frac{v-1}{v-1}. Whakareatia \frac{3}{v-1} ki te \frac{v+1}{v+1}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v\left(v-1\right)}{\left(v-1\right)\left(v+1\right)}+\frac{3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v\left(v-1\right)+3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}-v+3v+3}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1})$$

Whakakotahitia ngā kupu rite i v^{2}-v+3v+3.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1})$$

Tauwehea te v^{2}-1.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)}-\frac{6}{\left(v-1\right)\left(v+1\right)})$$

Tā te mea he rite te tauraro o \frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)} me \frac{6}{\left(v-1\right)\left(v+1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}+2v+3-6}{\left(v-1\right)\left(v+1\right)})$$

Whakakotahitia ngā kupu rite i v^{2}+2v+3-6.

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

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{v^{2}+2v-3}{\left(v-1\right)\left(v+1\right)}.

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

Me whakakore tahi te v-1 i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v+3}{v+1})$$

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.

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

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}.

$$\frac{\left(v^{1}+1\right)v^{1-1}-\left(v^{1}+3\right)v^{1-1}}{\left(v^{1}+1\right)^{2}}$$

Mahia ngā tātaitanga.

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

Whakarohaina mā te āhuatanga tohatoha.

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

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

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

Tangohia ngā taiapa kāore i te hiahiatia.

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

Pahekotia ngā kīanga tau ōrite.

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

Tangohia te 1 i 1 me te 3 i te 1.

$$\frac{-2v^{0}}{\left(v^{1}+1\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-2v^{0}}{\left(v+1\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

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