Whakaoti i te 6/x-4+5/x+3

$$\frac { 6 } { x - 4 } + \frac { 5 } { x + 3 }$$

Aromātai

$$\frac{11x-2}{\left(x-4\right)\left(x+3\right)}$$

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-4 me x+3 ko \left(x-4\right)\left(x+3\right). Whakareatia \frac{6}{x-4} ki te \frac{x+3}{x+3}. Whakareatia \frac{5}{x+3} ki te \frac{x-4}{x-4}.

$$\frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}+\frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)}$$

Tā te mea he rite te tauraro o \frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)} me \frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{6\left(x+3\right)+5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)}$$

Mahia ngā whakarea i roto o 6\left(x+3\right)+5\left(x-4\right).

$$\frac{6x+18+5x-20}{\left(x-4\right)\left(x+3\right)}$$

Whakakotahitia ngā kupu rite i 6x+18+5x-20.

$$\frac{11x-2}{\left(x-4\right)\left(x+3\right)}$$

Whakarohaina te \left(x-4\right)\left(x+3\right).

$$\frac{11x-2}{x^{2}-x-12}$$

Kimi Pārōnaki e ai ki x

$$\frac{-11x^{2}+4x-134}{\left(\left(x-4\right)\left(x+3\right)\right)^{2}}$$

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-4 me x+3 ko \left(x-4\right)\left(x+3\right). Whakareatia \frac{6}{x-4} ki te \frac{x+3}{x+3}. Whakareatia \frac{5}{x+3} ki te \frac{x-4}{x-4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}+\frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)})$$

Tā te mea he rite te tauraro o \frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)} me \frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6\left(x+3\right)+5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)})$$

Mahia ngā whakarea i roto o 6\left(x+3\right)+5\left(x-4\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x+18+5x-20}{\left(x-4\right)\left(x+3\right)})$$

Whakakotahitia ngā kupu rite i 6x+18+5x-20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x-2}{\left(x-4\right)\left(x+3\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-4 ki ia tau o x+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x-2}{x^{2}+3x-4x-12})$$

Pahekotia te 3x me -4x, ka -x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x-2}{x^{2}-x-12})$$

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.

$$\frac{\left(x^{2}-x^{1}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(11x^{1}-2)-\left(11x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-12)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-x^{1}-12\right)\times 11x^{1-1}-\left(11x^{1}-2\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}-x^{1}-12\right)\times 11x^{0}-\left(11x^{1}-2\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Whakareatia x^{2}-x^{1}-12 ki te 11x^{0}.

$$\frac{x^{2}\times 11x^{0}-x^{1}\times 11x^{0}-12\times 11x^{0}-\left(11x^{1}-2\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Whakareatia 11x^{1}-2 ki te 2x^{1}-x^{0}.

$$\frac{x^{2}\times 11x^{0}-x^{1}\times 11x^{0}-12\times 11x^{0}-\left(11x^{1}\times 2x^{1}+11x^{1}\left(-1\right)x^{0}-2\times 2x^{1}-2\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

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

$$\frac{11x^{2}-11x^{1}-12\times 11x^{0}-\left(11\times 2x^{1+1}+11\left(-1\right)x^{1}-2\times 2x^{1}-2\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Whakarūnātia.

$$\frac{11x^{2}-11x^{1}-132x^{0}-\left(22x^{2}-11x^{1}-4x^{1}+2x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-11x^{2}+4x^{1}-134x^{0}}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-11x^{2}+4x-134x^{0}}{\left(x^{2}-x-12\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-11x^{2}+4x-134}{\left(x^{2}-x-12\right)^{2}}$$