Whakaoti i te 5/w+1+8/w-7

$$\frac { 5 } { w + 1 } + \frac { 8 } { w - 7 }$$

Aromātai

$$\frac{13w-27}{\left(w-7\right)\left(w+1\right)}$$

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 w+1 me w-7 ko \left(w-7\right)\left(w+1\right). Whakareatia \frac{5}{w+1} ki te \frac{w-7}{w-7}. Whakareatia \frac{8}{w-7} ki te \frac{w+1}{w+1}.

$$\frac{5\left(w-7\right)}{\left(w-7\right)\left(w+1\right)}+\frac{8\left(w+1\right)}{\left(w-7\right)\left(w+1\right)}$$

Tā te mea he rite te tauraro o \frac{5\left(w-7\right)}{\left(w-7\right)\left(w+1\right)} me \frac{8\left(w+1\right)}{\left(w-7\right)\left(w+1\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5\left(w-7\right)+8\left(w+1\right)}{\left(w-7\right)\left(w+1\right)}$$

Mahia ngā whakarea i roto o 5\left(w-7\right)+8\left(w+1\right).

$$\frac{5w-35+8w+8}{\left(w-7\right)\left(w+1\right)}$$

Whakakotahitia ngā kupu rite i 5w-35+8w+8.

$$\frac{13w-27}{\left(w-7\right)\left(w+1\right)}$$

Whakarohaina te \left(w-7\right)\left(w+1\right).

$$\frac{13w-27}{w^{2}-6w-7}$$

Kimi Pārōnaki e ai ki w

$$\frac{-13w^{2}+54w-253}{\left(\left(w-7\right)\left(w+1\right)\right)^{2}}$$

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 w+1 me w-7 ko \left(w-7\right)\left(w+1\right). Whakareatia \frac{5}{w+1} ki te \frac{w-7}{w-7}. Whakareatia \frac{8}{w-7} ki te \frac{w+1}{w+1}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{5\left(w-7\right)}{\left(w-7\right)\left(w+1\right)}+\frac{8\left(w+1\right)}{\left(w-7\right)\left(w+1\right)})$$

Tā te mea he rite te tauraro o \frac{5\left(w-7\right)}{\left(w-7\right)\left(w+1\right)} me \frac{8\left(w+1\right)}{\left(w-7\right)\left(w+1\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{5\left(w-7\right)+8\left(w+1\right)}{\left(w-7\right)\left(w+1\right)})$$

Mahia ngā whakarea i roto o 5\left(w-7\right)+8\left(w+1\right).

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{5w-35+8w+8}{\left(w-7\right)\left(w+1\right)})$$

Whakakotahitia ngā kupu rite i 5w-35+8w+8.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{13w-27}{\left(w-7\right)\left(w+1\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o w-7 ki ia tau o w+1.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{13w-27}{w^{2}+w-7w-7})$$

Pahekotia te w me -7w, ka -6w.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{13w-27}{w^{2}-6w-7})$$

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.

$$\frac{\left(w^{2}-6w^{1}-7\right)\frac{\mathrm{d}}{\mathrm{d}w}(13w^{1}-27)-\left(13w^{1}-27\right)\frac{\mathrm{d}}{\mathrm{d}w}(w^{2}-6w^{1}-7)}{\left(w^{2}-6w^{1}-7\right)^{2}}$$

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}.

$$\frac{\left(w^{2}-6w^{1}-7\right)\times 13w^{1-1}-\left(13w^{1}-27\right)\left(2w^{2-1}-6w^{1-1}\right)}{\left(w^{2}-6w^{1}-7\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(w^{2}-6w^{1}-7\right)\times 13w^{0}-\left(13w^{1}-27\right)\left(2w^{1}-6w^{0}\right)}{\left(w^{2}-6w^{1}-7\right)^{2}}$$

Whakareatia w^{2}-6w^{1}-7 ki te 13w^{0}.

$$\frac{w^{2}\times 13w^{0}-6w^{1}\times 13w^{0}-7\times 13w^{0}-\left(13w^{1}-27\right)\left(2w^{1}-6w^{0}\right)}{\left(w^{2}-6w^{1}-7\right)^{2}}$$

Whakareatia 13w^{1}-27 ki te 2w^{1}-6w^{0}.

$$\frac{w^{2}\times 13w^{0}-6w^{1}\times 13w^{0}-7\times 13w^{0}-\left(13w^{1}\times 2w^{1}+13w^{1}\left(-6\right)w^{0}-27\times 2w^{1}-27\left(-6\right)w^{0}\right)}{\left(w^{2}-6w^{1}-7\right)^{2}}$$

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

$$\frac{13w^{2}-6\times 13w^{1}-7\times 13w^{0}-\left(13\times 2w^{1+1}+13\left(-6\right)w^{1}-27\times 2w^{1}-27\left(-6\right)w^{0}\right)}{\left(w^{2}-6w^{1}-7\right)^{2}}$$

Whakarūnātia.

$$\frac{13w^{2}-78w^{1}-91w^{0}-\left(26w^{2}-78w^{1}-54w^{1}+162w^{0}\right)}{\left(w^{2}-6w^{1}-7\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-13w^{2}+54w^{1}-253w^{0}}{\left(w^{2}-6w^{1}-7\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-13w^{2}+54w-253w^{0}}{\left(w^{2}-6w-7\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-13w^{2}+54w-253}{\left(w^{2}-6w-7\right)^{2}}$$