Whakaoti i te 1/2x-3+1/x-5=

$$\frac { 1 } { 2 x - 3 } + \frac { 1 } { x - 5 } =$$

Aromātai

$$\frac{3x-8}{\left(x-5\right)\left(2x-3\right)}$$

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 2x-3 me x-5 ko \left(x-5\right)\left(2x-3\right). Whakareatia \frac{1}{2x-3} ki te \frac{x-5}{x-5}. Whakareatia \frac{1}{x-5} ki te \frac{2x-3}{2x-3}.

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

Tā te mea he rite te tauraro o \frac{x-5}{\left(x-5\right)\left(2x-3\right)} me \frac{2x-3}{\left(x-5\right)\left(2x-3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Whakakotahitia ngā kupu rite i x-5+2x-3.

$$\frac{3x-8}{\left(x-5\right)\left(2x-3\right)}$$

Whakarohaina te \left(x-5\right)\left(2x-3\right).

$$\frac{3x-8}{2x^{2}-13x+15}$$

Kimi Pārōnaki e ai ki x

$$\frac{-6x^{2}+32x-59}{\left(\left(x-5\right)\left(2x-3\right)\right)^{2}}$$

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 2x-3 me x-5 ko \left(x-5\right)\left(2x-3\right). Whakareatia \frac{1}{2x-3} ki te \frac{x-5}{x-5}. Whakareatia \frac{1}{x-5} ki te \frac{2x-3}{2x-3}.

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

Tā te mea he rite te tauraro o \frac{x-5}{\left(x-5\right)\left(2x-3\right)} me \frac{2x-3}{\left(x-5\right)\left(2x-3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Whakakotahitia ngā kupu rite i x-5+2x-3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x-8}{\left(x-5\right)\left(2x-3\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-5 ki ia tau o 2x-3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x-8}{2x^{2}-3x-10x+15})$$

Pahekotia te -3x me -10x, ka -13x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x-8}{2x^{2}-13x+15})$$

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.

$$\frac{\left(2x^{2}-13x^{1}+15\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1}-8)-\left(3x^{1}-8\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-13x^{1}+15)}{\left(2x^{2}-13x^{1}+15\right)^{2}}$$

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}.

$$\frac{\left(2x^{2}-13x^{1}+15\right)\times 3x^{1-1}-\left(3x^{1}-8\right)\left(2\times 2x^{2-1}-13x^{1-1}\right)}{\left(2x^{2}-13x^{1}+15\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(2x^{2}-13x^{1}+15\right)\times 3x^{0}-\left(3x^{1}-8\right)\left(4x^{1}-13x^{0}\right)}{\left(2x^{2}-13x^{1}+15\right)^{2}}$$

Whakareatia 2x^{2}-13x^{1}+15 ki te 3x^{0}.

$$\frac{2x^{2}\times 3x^{0}-13x^{1}\times 3x^{0}+15\times 3x^{0}-\left(3x^{1}-8\right)\left(4x^{1}-13x^{0}\right)}{\left(2x^{2}-13x^{1}+15\right)^{2}}$$

Whakareatia 3x^{1}-8 ki te 4x^{1}-13x^{0}.

$$\frac{2x^{2}\times 3x^{0}-13x^{1}\times 3x^{0}+15\times 3x^{0}-\left(3x^{1}\times 4x^{1}+3x^{1}\left(-13\right)x^{0}-8\times 4x^{1}-8\left(-13\right)x^{0}\right)}{\left(2x^{2}-13x^{1}+15\right)^{2}}$$

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

$$\frac{2\times 3x^{2}-13\times 3x^{1}+15\times 3x^{0}-\left(3\times 4x^{1+1}+3\left(-13\right)x^{1}-8\times 4x^{1}-8\left(-13\right)x^{0}\right)}{\left(2x^{2}-13x^{1}+15\right)^{2}}$$

Whakarūnātia.

$$\frac{6x^{2}-39x^{1}+45x^{0}-\left(12x^{2}-39x^{1}-32x^{1}+104x^{0}\right)}{\left(2x^{2}-13x^{1}+15\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-6x^{2}+32x^{1}-59x^{0}}{\left(2x^{2}-13x^{1}+15\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-6x^{2}+32x-59x^{0}}{\left(2x^{2}-13x+15\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-6x^{2}+32x-59}{\left(2x^{2}-13x+15\right)^{2}}$$