Whakaoti i te 7/w^2-9+2/w-3

$$\frac { 7 } { w ^ { 2 } - 9 } + \frac { 2 } { w - 3 }$$

Aromātai

$$\frac{2w+13}{w^{2}-9}$$

Ngā Hipanga Rongoā Poto

Tauwehea te w^{2}-9.

$$\frac{7}{\left(w-3\right)\left(w+3\right)}+\frac{2}{w-3}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(w-3\right)\left(w+3\right) me w-3 ko \left(w-3\right)\left(w+3\right). Whakareatia \frac{2}{w-3} ki te \frac{w+3}{w+3}.

$$\frac{7}{\left(w-3\right)\left(w+3\right)}+\frac{2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)}$$

Tā te mea he rite te tauraro o \frac{7}{\left(w-3\right)\left(w+3\right)} me \frac{2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7+2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)}$$

Mahia ngā whakarea i roto o 7+2\left(w+3\right).

$$\frac{7+2w+6}{\left(w-3\right)\left(w+3\right)}$$

Whakakotahitia ngā kupu rite i 7+2w+6.

$$\frac{13+2w}{\left(w-3\right)\left(w+3\right)}$$

Whakarohaina te \left(w-3\right)\left(w+3\right).

$$\frac{13+2w}{w^{2}-9}$$

Kimi Pārōnaki e ai ki w

$$-\frac{2\left(w^{2}+13w+9\right)}{\left(w^{2}-9\right)^{2}}$$

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

Tauwehea te w^{2}-9.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{7}{\left(w-3\right)\left(w+3\right)}+\frac{2}{w-3})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(w-3\right)\left(w+3\right) me w-3 ko \left(w-3\right)\left(w+3\right). Whakareatia \frac{2}{w-3} ki te \frac{w+3}{w+3}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{7}{\left(w-3\right)\left(w+3\right)}+\frac{2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)})$$

Tā te mea he rite te tauraro o \frac{7}{\left(w-3\right)\left(w+3\right)} me \frac{2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{7+2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)})$$

Mahia ngā whakarea i roto o 7+2\left(w+3\right).

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{7+2w+6}{\left(w-3\right)\left(w+3\right)})$$

Whakakotahitia ngā kupu rite i 7+2w+6.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{13+2w}{\left(w-3\right)\left(w+3\right)})$$

Whakaarohia te \left(w-3\right)\left(w+3\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 3.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{13+2w}{w^{2}-9})$$

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.

$$\frac{\left(w^{2}-9\right)\frac{\mathrm{d}}{\mathrm{d}w}(2w^{1}+13)-\left(2w^{1}+13\right)\frac{\mathrm{d}}{\mathrm{d}w}(w^{2}-9)}{\left(w^{2}-9\right)^{2}}$$

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}.

$$\frac{\left(w^{2}-9\right)\times 2w^{1-1}-\left(2w^{1}+13\right)\times 2w^{2-1}}{\left(w^{2}-9\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(w^{2}-9\right)\times 2w^{0}-\left(2w^{1}+13\right)\times 2w^{1}}{\left(w^{2}-9\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{w^{2}\times 2w^{0}-9\times 2w^{0}-\left(2w^{1}\times 2w^{1}+13\times 2w^{1}\right)}{\left(w^{2}-9\right)^{2}}$$

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

$$\frac{2w^{2}-9\times 2w^{0}-\left(2\times 2w^{1+1}+13\times 2w^{1}\right)}{\left(w^{2}-9\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{2w^{2}-18w^{0}-\left(4w^{2}+26w^{1}\right)}{\left(w^{2}-9\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{2w^{2}-18w^{0}-4w^{2}-26w^{1}}{\left(w^{2}-9\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(2-4\right)w^{2}-18w^{0}-26w^{1}}{\left(w^{2}-9\right)^{2}}$$

Tango 4 mai i 2.

$$\frac{-2w^{2}-18w^{0}-26w^{1}}{\left(w^{2}-9\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-2w^{2}-18w^{0}-26w}{\left(w^{2}-9\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-2w^{2}-18-26w}{\left(w^{2}-9\right)^{2}}$$