Whakaoti i te 5x/x^2-9+2/x+3

$$\frac { 5 x } { x ^ { 2 } - 9 } + \frac { 2 } { x + 3 }$$

Aromātai

$$\frac{7x-6}{x^{2}-9}$$

Ngā Hipanga Rongoā Poto

Tauwehea te x^{2}-9.

$$\frac{5x}{\left(x-3\right)\left(x+3\right)}+\frac{2}{x+3}$$

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

$$\frac{5x}{\left(x-3\right)\left(x+3\right)}+\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}$$

Tā te mea he rite te tauraro o \frac{5x}{\left(x-3\right)\left(x+3\right)} me \frac{2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5x+2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}$$

Mahia ngā whakarea i roto o 5x+2\left(x-3\right).

$$\frac{5x+2x-6}{\left(x-3\right)\left(x+3\right)}$$

Whakakotahitia ngā kupu rite i 5x+2x-6.

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

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

$$\frac{7x-6}{x^{2}-9}$$

Kimi Pārōnaki e ai ki x

$$\frac{-7x^{2}+12x-63}{\left(x^{2}-9\right)^{2}}$$

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

Tauwehea te x^{2}-9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{\left(x-3\right)\left(x+3\right)}+\frac{2}{x+3})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{\left(x-3\right)\left(x+3\right)}+\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)})$$

Tā te mea he rite te tauraro o \frac{5x}{\left(x-3\right)\left(x+3\right)} me \frac{2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x+2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)})$$

Mahia ngā whakarea i roto o 5x+2\left(x-3\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x+2x-6}{\left(x-3\right)\left(x+3\right)})$$

Whakakotahitia ngā kupu rite i 5x+2x-6.

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

Whakaarohia te \left(x-3\right)\left(x+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.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-6}{x^{2}-9})$$

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.

$$\frac{\left(x^{2}-9\right)\frac{\mathrm{d}}{\mathrm{d}x}(7x^{1}-6)-\left(7x^{1}-6\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-9)}{\left(x^{2}-9\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-9\right)\times 7x^{1-1}-\left(7x^{1}-6\right)\times 2x^{2-1}}{\left(x^{2}-9\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(x^{2}-9\right)\times 7x^{0}-\left(7x^{1}-6\right)\times 2x^{1}}{\left(x^{2}-9\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{x^{2}\times 7x^{0}-9\times 7x^{0}-\left(7x^{1}\times 2x^{1}-6\times 2x^{1}\right)}{\left(x^{2}-9\right)^{2}}$$

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

$$\frac{7x^{2}-9\times 7x^{0}-\left(7\times 2x^{1+1}-6\times 2x^{1}\right)}{\left(x^{2}-9\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{7x^{2}-63x^{0}-\left(14x^{2}-12x^{1}\right)}{\left(x^{2}-9\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{7x^{2}-63x^{0}-14x^{2}-\left(-12x^{1}\right)}{\left(x^{2}-9\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(7-14\right)x^{2}-63x^{0}-\left(-12x^{1}\right)}{\left(x^{2}-9\right)^{2}}$$

Tango 14 mai i 7.

$$\frac{-7x^{2}-63x^{0}-\left(-12x^{1}\right)}{\left(x^{2}-9\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-7x^{2}-63x^{0}-\left(-12x\right)}{\left(x^{2}-9\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-7x^{2}-63-\left(-12x\right)}{\left(x^{2}-9\right)^{2}}$$