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

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

Aromātai

$$-\frac{5\left(x+4\right)}{\left(x-3\right)\left(x+2\right)}$$

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

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

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

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

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

$$\frac{2x-6-7x-14}{\left(x-3\right)\left(x+2\right)}$$

Whakakotahitia ngā kupu rite i 2x-6-7x-14.

$$\frac{-5x-20}{\left(x-3\right)\left(x+2\right)}$$

Whakarohaina te \left(x-3\right)\left(x+2\right).

$$\frac{-5x-20}{x^{2}-x-6}$$

Kimi Pārōnaki e ai ki x

$$\frac{5\left(\left(x+4\right)^{2}-14\right)}{\left(\left(x-3\right)\left(x+2\right)\right)^{2}}$$

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-6-7x-14}{\left(x-3\right)\left(x+2\right)})$$

Whakakotahitia ngā kupu rite i 2x-6-7x-14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x-20}{\left(x-3\right)\left(x+2\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-3 ki ia tau o x+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x-20}{x^{2}+2x-3x-6})$$

Pahekotia te 2x me -3x, ka -x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x-20}{x^{2}-x-6})$$

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.

$$\frac{\left(x^{2}-x^{1}-6\right)\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{1}-20)-\left(-5x^{1}-20\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-6)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-x^{1}-6\right)\left(-5\right)x^{1-1}-\left(-5x^{1}-20\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}-x^{1}-6\right)\left(-5\right)x^{0}-\left(-5x^{1}-20\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Whakareatia x^{2}-x^{1}-6 ki te -5x^{0}.

$$\frac{x^{2}\left(-5\right)x^{0}-x^{1}\left(-5\right)x^{0}-6\left(-5\right)x^{0}-\left(-5x^{1}-20\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Whakareatia -5x^{1}-20 ki te 2x^{1}-x^{0}.

$$\frac{x^{2}\left(-5\right)x^{0}-x^{1}\left(-5\right)x^{0}-6\left(-5\right)x^{0}-\left(-5x^{1}\times 2x^{1}-5x^{1}\left(-1\right)x^{0}-20\times 2x^{1}-20\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

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

$$\frac{-5x^{2}-\left(-5x^{1}\right)-6\left(-5\right)x^{0}-\left(-5\times 2x^{1+1}-5\left(-1\right)x^{1}-20\times 2x^{1}-20\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Whakarūnātia.

$$\frac{-5x^{2}+5x^{1}+30x^{0}-\left(-10x^{2}+5x^{1}-40x^{1}+20x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{5x^{2}+40x^{1}+10x^{0}}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{5x^{2}+40x+10x^{0}}{\left(x^{2}-x-6\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{5x^{2}+40x+10\times 1}{\left(x^{2}-x-6\right)^{2}}$$

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

$$\frac{5x^{2}+40x+10}{\left(x^{2}-x-6\right)^{2}}$$