Whakaoti i te 2/y^2-16-3/y+4

$$\frac { 2 } { y ^ { 2 } - 16 } - \frac { 3 } { y + 4 }$$

Aromātai

$$\frac{14-3y}{y^{2}-16}$$

Ngā Hipanga Rongoā Poto

Tauwehea te y^{2}-16.

$$\frac{2}{\left(y-4\right)\left(y+4\right)}-\frac{3}{y+4}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(y-4\right)\left(y+4\right) me y+4 ko \left(y-4\right)\left(y+4\right). Whakareatia \frac{3}{y+4} ki te \frac{y-4}{y-4}.

$$\frac{2}{\left(y-4\right)\left(y+4\right)}-\frac{3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}$$

Tā te mea he rite te tauraro o \frac{2}{\left(y-4\right)\left(y+4\right)} me \frac{3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2-3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}$$

Mahia ngā whakarea i roto o 2-3\left(y-4\right).

$$\frac{2-3y+12}{\left(y-4\right)\left(y+4\right)}$$

Whakakotahitia ngā kupu rite i 2-3y+12.

$$\frac{14-3y}{\left(y-4\right)\left(y+4\right)}$$

Whakarohaina te \left(y-4\right)\left(y+4\right).

$$\frac{14-3y}{y^{2}-16}$$

Kimi Pārōnaki e ai ki y

$$\frac{3y^{2}-28y+48}{\left(y^{2}-16\right)^{2}}$$

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

Tauwehea te y^{2}-16.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2}{\left(y-4\right)\left(y+4\right)}-\frac{3}{y+4})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(y-4\right)\left(y+4\right) me y+4 ko \left(y-4\right)\left(y+4\right). Whakareatia \frac{3}{y+4} ki te \frac{y-4}{y-4}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2}{\left(y-4\right)\left(y+4\right)}-\frac{3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)})$$

Tā te mea he rite te tauraro o \frac{2}{\left(y-4\right)\left(y+4\right)} me \frac{3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2-3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)})$$

Mahia ngā whakarea i roto o 2-3\left(y-4\right).

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2-3y+12}{\left(y-4\right)\left(y+4\right)})$$

Whakakotahitia ngā kupu rite i 2-3y+12.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{14-3y}{\left(y-4\right)\left(y+4\right)})$$

Whakaarohia te \left(y-4\right)\left(y+4\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 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{14-3y}{y^{2}-16})$$

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.

$$\frac{\left(y^{2}-16\right)\frac{\mathrm{d}}{\mathrm{d}y}(-3y^{1}+14)-\left(-3y^{1}+14\right)\frac{\mathrm{d}}{\mathrm{d}y}(y^{2}-16)}{\left(y^{2}-16\right)^{2}}$$

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}.

$$\frac{\left(y^{2}-16\right)\left(-3\right)y^{1-1}-\left(-3y^{1}+14\right)\times 2y^{2-1}}{\left(y^{2}-16\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(y^{2}-16\right)\left(-3\right)y^{0}-\left(-3y^{1}+14\right)\times 2y^{1}}{\left(y^{2}-16\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{y^{2}\left(-3\right)y^{0}-16\left(-3\right)y^{0}-\left(-3y^{1}\times 2y^{1}+14\times 2y^{1}\right)}{\left(y^{2}-16\right)^{2}}$$

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

$$\frac{-3y^{2}-16\left(-3\right)y^{0}-\left(-3\times 2y^{1+1}+14\times 2y^{1}\right)}{\left(y^{2}-16\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{-3y^{2}+48y^{0}-\left(-6y^{2}+28y^{1}\right)}{\left(y^{2}-16\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{-3y^{2}+48y^{0}-\left(-6y^{2}\right)-28y^{1}}{\left(y^{2}-16\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(-3-\left(-6\right)\right)y^{2}+48y^{0}-28y^{1}}{\left(y^{2}-16\right)^{2}}$$

Tango -6 mai i -3.

$$\frac{3y^{2}+48y^{0}-28y^{1}}{\left(y^{2}-16\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{3y^{2}+48y^{0}-28y}{\left(y^{2}-16\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{3y^{2}+48\times 1-28y}{\left(y^{2}-16\right)^{2}}$$

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

$$\frac{3y^{2}+48-28y}{\left(y^{2}-16\right)^{2}}$$