Whakaoti i te 3/x-6-2/x+2

$$\frac { 3 } { x - 6 } - \frac { 2 } { x + 2 }$$

Aromātai

$$\frac{x+18}{\left(x-6\right)\left(x+2\right)}$$

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 x-6 me x+2 ko \left(x-6\right)\left(x+2\right). Whakareatia \frac{3}{x-6} ki te \frac{x+2}{x+2}. Whakareatia \frac{2}{x+2} ki te \frac{x-6}{x-6}.

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

Tā te mea he rite te tauraro o \frac{3\left(x+2\right)}{\left(x-6\right)\left(x+2\right)} me \frac{2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 3\left(x+2\right)-2\left(x-6\right).

$$\frac{3x+6-2x+12}{\left(x-6\right)\left(x+2\right)}$$

Whakakotahitia ngā kupu rite i 3x+6-2x+12.

$$\frac{x+18}{\left(x-6\right)\left(x+2\right)}$$

Whakarohaina te \left(x-6\right)\left(x+2\right).

$$\frac{x+18}{x^{2}-4x-12}$$

Kimi Pārōnaki e ai ki x

$$\frac{60-36x-x^{2}}{x^{4}-8x^{3}-8x^{2}+96x+144}$$

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 x-6 me x+2 ko \left(x-6\right)\left(x+2\right). Whakareatia \frac{3}{x-6} ki te \frac{x+2}{x+2}. Whakareatia \frac{2}{x+2} ki te \frac{x-6}{x-6}.

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

Tā te mea he rite te tauraro o \frac{3\left(x+2\right)}{\left(x-6\right)\left(x+2\right)} me \frac{2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 3\left(x+2\right)-2\left(x-6\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+6-2x+12}{\left(x-6\right)\left(x+2\right)})$$

Whakakotahitia ngā kupu rite i 3x+6-2x+12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+18}{\left(x-6\right)\left(x+2\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-6 ki ia tau o x+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+18}{x^{2}+2x-6x-12})$$

Pahekotia te 2x me -6x, ka -4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+18}{x^{2}-4x-12})$$

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.

$$\frac{\left(x^{2}-4x^{1}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+18)-\left(x^{1}+18\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x^{1}-12)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-4x^{1}-12\right)x^{1-1}-\left(x^{1}+18\right)\left(2x^{2-1}-4x^{1-1}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}-4x^{1}-12\right)x^{0}-\left(x^{1}+18\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Whakareatia x^{2}-4x^{1}-12 ki te x^{0}.

$$\frac{x^{2}x^{0}-4x^{1}x^{0}-12x^{0}-\left(x^{1}+18\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Whakareatia x^{1}+18 ki te 2x^{1}-4x^{0}.

$$\frac{x^{2}x^{0}-4x^{1}x^{0}-12x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\left(-4\right)x^{0}+18\times 2x^{1}+18\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

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

$$\frac{x^{2}-4x^{1}-12x^{0}-\left(2x^{1+1}-4x^{1}+18\times 2x^{1}+18\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Whakarūnātia.

$$\frac{x^{2}-4x^{1}-12x^{0}-\left(2x^{2}-4x^{1}+36x^{1}-72x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-x^{2}-36x^{1}+60x^{0}}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-x^{2}-36x+60x^{0}}{\left(x^{2}-4x-12\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-x^{2}-36x+60\times 1}{\left(x^{2}-4x-12\right)^{2}}$$

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

$$\frac{-x^{2}-36x+60}{\left(x^{2}-4x-12\right)^{2}}$$