Whakaoti i te x/x^2-100+2/10-x

$$\frac { x } { x ^ { 2 } - 100 } + \frac { 2 } { 10 - x }$$

Aromātai

$$\frac{x+20}{100-x^{2}}$$

Ngā Hipanga Rongoā Poto

Tauwehea te x^{2}-100.

$$\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2}{10-x}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(x-10\right)\left(x+10\right) me 10-x ko \left(x-10\right)\left(x+10\right). Whakareatia \frac{2}{10-x} ki te \frac{-\left(x+10\right)}{-\left(x+10\right)}.

$$\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)}$$

Tā te mea he rite te tauraro o \frac{x}{\left(x-10\right)\left(x+10\right)} me \frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{x+2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)}$$

Mahia ngā whakarea i roto o x+2\left(-1\right)\left(x+10\right).

$$\frac{x-2x-20}{\left(x-10\right)\left(x+10\right)}$$

Whakakotahitia ngā kupu rite i x-2x-20.

$$\frac{-x-20}{\left(x-10\right)\left(x+10\right)}$$

Whakarohaina te \left(x-10\right)\left(x+10\right).

$$\frac{-x-20}{x^{2}-100}$$

Kimi Pārōnaki e ai ki x

$$\frac{x^{2}+40x+100}{\left(100-x^{2}\right)^{2}}$$

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

Tauwehea te x^{2}-100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2}{10-x})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(x-10\right)\left(x+10\right) me 10-x ko \left(x-10\right)\left(x+10\right). Whakareatia \frac{2}{10-x} ki te \frac{-\left(x+10\right)}{-\left(x+10\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)})$$

Tā te mea he rite te tauraro o \frac{x}{\left(x-10\right)\left(x+10\right)} me \frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)})$$

Mahia ngā whakarea i roto o x+2\left(-1\right)\left(x+10\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-2x-20}{\left(x-10\right)\left(x+10\right)})$$

Whakakotahitia ngā kupu rite i x-2x-20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x-20}{\left(x-10\right)\left(x+10\right)})$$

Whakaarohia te \left(x-10\right)\left(x+10\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 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x-20}{x^{2}-100})$$

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.

$$\frac{\left(x^{2}-100\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}-20)-\left(-x^{1}-20\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-100)}{\left(x^{2}-100\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-100\right)\left(-1\right)x^{1-1}-\left(-x^{1}-20\right)\times 2x^{2-1}}{\left(x^{2}-100\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(x^{2}-100\right)\left(-1\right)x^{0}-\left(-x^{1}-20\right)\times 2x^{1}}{\left(x^{2}-100\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{x^{2}\left(-1\right)x^{0}-100\left(-1\right)x^{0}-\left(-x^{1}\times 2x^{1}-20\times 2x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{-x^{2}-100\left(-1\right)x^{0}-\left(-2x^{1+1}-20\times 2x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{-x^{2}+100x^{0}-\left(-2x^{2}-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{-x^{2}+100x^{0}-\left(-2x^{2}\right)-\left(-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(-1-\left(-2\right)\right)x^{2}+100x^{0}-\left(-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Tango -2 mai i -1.

$$\frac{x^{2}+100x^{0}-\left(-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{x^{2}+100x^{0}-\left(-40x\right)}{\left(x^{2}-100\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{x^{2}+100\times 1-\left(-40x\right)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{x^{2}+100-\left(-40x\right)}{\left(x^{2}-100\right)^{2}}$$