Whakaoti i te 4/x-7+3/x+2

$$\frac { 4 } { x - 7 } + \frac { 3 } { x + 2 }$$

Aromātai

$$\frac{7x-13}{\left(x-7\right)\left(x+2\right)}$$

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-7 me x+2 ko \left(x-7\right)\left(x+2\right). Whakareatia \frac{4}{x-7} ki te \frac{x+2}{x+2}. Whakareatia \frac{3}{x+2} ki te \frac{x-7}{x-7}.

$$\frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)}+\frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)}$$

Tā te mea he rite te tauraro o \frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)} me \frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4\left(x+2\right)+3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)}$$

Mahia ngā whakarea i roto o 4\left(x+2\right)+3\left(x-7\right).

$$\frac{4x+8+3x-21}{\left(x-7\right)\left(x+2\right)}$$

Whakakotahitia ngā kupu rite i 4x+8+3x-21.

$$\frac{7x-13}{\left(x-7\right)\left(x+2\right)}$$

Whakarohaina te \left(x-7\right)\left(x+2\right).

$$\frac{7x-13}{x^{2}-5x-14}$$

Kimi Pārōnaki e ai ki x

$$\frac{-7x^{2}+26x-163}{\left(\left(x-7\right)\left(x+2\right)\right)^{2}}$$

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-7 me x+2 ko \left(x-7\right)\left(x+2\right). Whakareatia \frac{4}{x-7} ki te \frac{x+2}{x+2}. Whakareatia \frac{3}{x+2} ki te \frac{x-7}{x-7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)}+\frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)})$$

Tā te mea he rite te tauraro o \frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)} me \frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+2\right)+3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)})$$

Mahia ngā whakarea i roto o 4\left(x+2\right)+3\left(x-7\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+8+3x-21}{\left(x-7\right)\left(x+2\right)})$$

Whakakotahitia ngā kupu rite i 4x+8+3x-21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-13}{\left(x-7\right)\left(x+2\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-7 ki ia tau o x+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-13}{x^{2}+2x-7x-14})$$

Pahekotia te 2x me -7x, ka -5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-13}{x^{2}-5x-14})$$

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.

$$\frac{\left(x^{2}-5x^{1}-14\right)\frac{\mathrm{d}}{\mathrm{d}x}(7x^{1}-13)-\left(7x^{1}-13\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-5x^{1}-14)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-5x^{1}-14\right)\times 7x^{1-1}-\left(7x^{1}-13\right)\left(2x^{2-1}-5x^{1-1}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}-5x^{1}-14\right)\times 7x^{0}-\left(7x^{1}-13\right)\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Whakareatia x^{2}-5x^{1}-14 ki te 7x^{0}.

$$\frac{x^{2}\times 7x^{0}-5x^{1}\times 7x^{0}-14\times 7x^{0}-\left(7x^{1}-13\right)\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Whakareatia 7x^{1}-13 ki te 2x^{1}-5x^{0}.

$$\frac{x^{2}\times 7x^{0}-5x^{1}\times 7x^{0}-14\times 7x^{0}-\left(7x^{1}\times 2x^{1}+7x^{1}\left(-5\right)x^{0}-13\times 2x^{1}-13\left(-5\right)x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

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

$$\frac{7x^{2}-5\times 7x^{1}-14\times 7x^{0}-\left(7\times 2x^{1+1}+7\left(-5\right)x^{1}-13\times 2x^{1}-13\left(-5\right)x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Whakarūnātia.

$$\frac{7x^{2}-35x^{1}-98x^{0}-\left(14x^{2}-35x^{1}-26x^{1}+65x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-7x^{2}+26x^{1}-163x^{0}}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-7x^{2}+26x-163x^{0}}{\left(x^{2}-5x-14\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-7x^{2}+26x-163}{\left(x^{2}-5x-14\right)^{2}}$$