Whakaoti i te 2/x-2+3/x+1

$$\frac { 2 } { x - 2 } + \frac { 3 } { x + 1 }$$

Aromātai

$$\frac{5x-4}{\left(x-2\right)\left(x+1\right)}$$

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-2 me x+1 ko \left(x-2\right)\left(x+1\right). Whakareatia \frac{2}{x-2} ki te \frac{x+1}{x+1}. Whakareatia \frac{3}{x+1} ki te \frac{x-2}{x-2}.

$$\frac{2\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}+\frac{3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}$$

Tā te mea he rite te tauraro o \frac{2\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} me \frac{3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2\left(x+1\right)+3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}$$

Mahia ngā whakarea i roto o 2\left(x+1\right)+3\left(x-2\right).

$$\frac{2x+2+3x-6}{\left(x-2\right)\left(x+1\right)}$$

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

$$\frac{5x-4}{\left(x-2\right)\left(x+1\right)}$$

Whakarohaina te \left(x-2\right)\left(x+1\right).

$$\frac{5x-4}{x^{2}-x-2}$$

Kimi Pārōnaki e ai ki x

$$\frac{-5x^{2}+8x-14}{\left(\left(x-2\right)\left(x+1\right)\right)^{2}}$$

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-2 me x+1 ko \left(x-2\right)\left(x+1\right). Whakareatia \frac{2}{x-2} ki te \frac{x+1}{x+1}. Whakareatia \frac{3}{x+1} ki te \frac{x-2}{x-2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}+\frac{3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)})$$

Tā te mea he rite te tauraro o \frac{2\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} me \frac{3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x+1\right)+3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)})$$

Mahia ngā whakarea i roto o 2\left(x+1\right)+3\left(x-2\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+2+3x-6}{\left(x-2\right)\left(x+1\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-4}{\left(x-2\right)\left(x+1\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-2 ki ia tau o x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-4}{x^{2}+x-2x-2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-4}{x^{2}-x-2})$$

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.

$$\frac{\left(x^{2}-x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1}-4)-\left(5x^{1}-4\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-2)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-x^{1}-2\right)\times 5x^{1-1}-\left(5x^{1}-4\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}-x^{1}-2\right)\times 5x^{0}-\left(5x^{1}-4\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Whakareatia x^{2}-x^{1}-2 ki te 5x^{0}.

$$\frac{x^{2}\times 5x^{0}-x^{1}\times 5x^{0}-2\times 5x^{0}-\left(5x^{1}-4\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Whakareatia 5x^{1}-4 ki te 2x^{1}-x^{0}.

$$\frac{x^{2}\times 5x^{0}-x^{1}\times 5x^{0}-2\times 5x^{0}-\left(5x^{1}\times 2x^{1}+5x^{1}\left(-1\right)x^{0}-4\times 2x^{1}-4\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{5x^{2}-5x^{1}-2\times 5x^{0}-\left(5\times 2x^{1+1}+5\left(-1\right)x^{1}-4\times 2x^{1}-4\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Whakarūnātia.

$$\frac{5x^{2}-5x^{1}-10x^{0}-\left(10x^{2}-5x^{1}-8x^{1}+4x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-5x^{2}+8x^{1}-14x^{0}}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-5x^{2}+8x-14x^{0}}{\left(x^{2}-x-2\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-5x^{2}+8x-14}{\left(x^{2}-x-2\right)^{2}}$$