Whakaoti i te v/v^2+17v+72-8/v^2+15v+56

$$\frac { v } { v ^ { 2 } + 17 v + 72 } - \frac { 8 } { v ^ { 2 } + 15 v + 56 }$$

Aromātai

$$\frac{v-9}{\left(v+7\right)\left(v+9\right)}$$

Ngā Hipanga Rongoā Poto

Tauwehea te v^{2}+17v+72. Tauwehea te v^{2}+15v+56.

$$\frac{v}{\left(v+8\right)\left(v+9\right)}-\frac{8}{\left(v+7\right)\left(v+8\right)}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(v+8\right)\left(v+9\right) me \left(v+7\right)\left(v+8\right) ko \left(v+7\right)\left(v+8\right)\left(v+9\right). Whakareatia \frac{v}{\left(v+8\right)\left(v+9\right)} ki te \frac{v+7}{v+7}. Whakareatia \frac{8}{\left(v+7\right)\left(v+8\right)} ki te \frac{v+9}{v+9}.

$$\frac{v\left(v+7\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}-\frac{8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

Tā te mea he rite te tauraro o \frac{v\left(v+7\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)} me \frac{8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{v\left(v+7\right)-8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

Mahia ngā whakarea i roto o v\left(v+7\right)-8\left(v+9\right).

$$\frac{v^{2}+7v-8v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

Whakakotahitia ngā kupu rite i v^{2}+7v-8v-72.

$$\frac{v^{2}-v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{v^{2}-v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}.

$$\frac{\left(v-9\right)\left(v+8\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

Me whakakore tahi te v+8 i te taurunga me te tauraro.

$$\frac{v-9}{\left(v+7\right)\left(v+9\right)}$$

Whakarohaina te \left(v+7\right)\left(v+9\right).

$$\frac{v-9}{v^{2}+16v+63}$$

Kimi Pārōnaki e ai ki v

$$\frac{207+18v-v^{2}}{v^{4}+32v^{3}+382v^{2}+2016v+3969}$$

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

Tauwehea te v^{2}+17v+72. Tauwehea te v^{2}+15v+56.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v}{\left(v+8\right)\left(v+9\right)}-\frac{8}{\left(v+7\right)\left(v+8\right)})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(v+8\right)\left(v+9\right) me \left(v+7\right)\left(v+8\right) ko \left(v+7\right)\left(v+8\right)\left(v+9\right). Whakareatia \frac{v}{\left(v+8\right)\left(v+9\right)} ki te \frac{v+7}{v+7}. Whakareatia \frac{8}{\left(v+7\right)\left(v+8\right)} ki te \frac{v+9}{v+9}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v\left(v+7\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}-\frac{8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

Tā te mea he rite te tauraro o \frac{v\left(v+7\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)} me \frac{8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v\left(v+7\right)-8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

Mahia ngā whakarea i roto o v\left(v+7\right)-8\left(v+9\right).

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}+7v-8v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

Whakakotahitia ngā kupu rite i v^{2}+7v-8v-72.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}-v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{v^{2}-v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{\left(v-9\right)\left(v+8\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

Me whakakore tahi te v+8 i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v-9}{\left(v+7\right)\left(v+9\right)})$$

Whakamahia te āhuatanga tuaritanga hei whakarea te v+7 ki te v+9 ka whakakotahi i ngā kupu rite.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v-9}{v^{2}+16v+63})$$

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.

$$\frac{\left(v^{2}+16v^{1}+63\right)\frac{\mathrm{d}}{\mathrm{d}v}(v^{1}-9)-\left(v^{1}-9\right)\frac{\mathrm{d}}{\mathrm{d}v}(v^{2}+16v^{1}+63)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

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}.

$$\frac{\left(v^{2}+16v^{1}+63\right)v^{1-1}-\left(v^{1}-9\right)\left(2v^{2-1}+16v^{1-1}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(v^{2}+16v^{1}+63\right)v^{0}-\left(v^{1}-9\right)\left(2v^{1}+16v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

Whakareatia v^{2}+16v^{1}+63 ki te v^{0}.

$$\frac{v^{2}v^{0}+16v^{1}v^{0}+63v^{0}-\left(v^{1}-9\right)\left(2v^{1}+16v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

Whakareatia v^{1}-9 ki te 2v^{1}+16v^{0}.

$$\frac{v^{2}v^{0}+16v^{1}v^{0}+63v^{0}-\left(v^{1}\times 2v^{1}+v^{1}\times 16v^{0}-9\times 2v^{1}-9\times 16v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

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

$$\frac{v^{2}+16v^{1}+63v^{0}-\left(2v^{1+1}+16v^{1}-9\times 2v^{1}-9\times 16v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

Whakarūnātia.

$$\frac{v^{2}+16v^{1}+63v^{0}-\left(2v^{2}+16v^{1}-18v^{1}-144v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-v^{2}+18v^{1}+207v^{0}}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-v^{2}+18v+207v^{0}}{\left(v^{2}+16v+63\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-v^{2}+18v+207\times 1}{\left(v^{2}+16v+63\right)^{2}}$$

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

$$\frac{-v^{2}+18v+207}{\left(v^{2}+16v+63\right)^{2}}$$