Whakaoti i te 3/2x-5-4/x-3

$$\frac{ 3 }{ 2x-5 } - \frac{ 4 }{ x-3 }$$

Aromātai

$$\frac{11-5x}{\left(x-3\right)\left(2x-5\right)}$$

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-5 me x-3 ko \left(x-3\right)\left(2x-5\right). Whakareatia \frac{3}{2x-5} ki te \frac{x-3}{x-3}. Whakareatia \frac{4}{x-3} ki te \frac{2x-5}{2x-5}.

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

Tā te mea he rite te tauraro o \frac{3\left(x-3\right)}{\left(x-3\right)\left(2x-5\right)} me \frac{4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 3\left(x-3\right)-4\left(2x-5\right).

$$\frac{3x-9-8x+20}{\left(x-3\right)\left(2x-5\right)}$$

Whakakotahitia ngā kupu rite i 3x-9-8x+20.

$$\frac{-5x+11}{\left(x-3\right)\left(2x-5\right)}$$

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

$$\frac{-5x+11}{2x^{2}-11x+15}$$

Kimi Pārōnaki e ai ki x

$$\frac{2\left(\left(5x-11\right)^{2}-6\right)}{5\left(\left(x-3\right)\left(2x-5\right)\right)^{2}}$$

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-5 me x-3 ko \left(x-3\right)\left(2x-5\right). Whakareatia \frac{3}{2x-5} ki te \frac{x-3}{x-3}. Whakareatia \frac{4}{x-3} ki te \frac{2x-5}{2x-5}.

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

Tā te mea he rite te tauraro o \frac{3\left(x-3\right)}{\left(x-3\right)\left(2x-5\right)} me \frac{4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 3\left(x-3\right)-4\left(2x-5\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x-9-8x+20}{\left(x-3\right)\left(2x-5\right)})$$

Whakakotahitia ngā kupu rite i 3x-9-8x+20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x+11}{\left(x-3\right)\left(2x-5\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x+11}{2x^{2}-5x-6x+15})$$

Pahekotia te -5x me -6x, ka -11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x+11}{2x^{2}-11x+15})$$

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.

$$\frac{\left(2x^{2}-11x^{1}+15\right)\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{1}+11)-\left(-5x^{1}+11\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-11x^{1}+15)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

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}.

$$\frac{\left(2x^{2}-11x^{1}+15\right)\left(-5\right)x^{1-1}-\left(-5x^{1}+11\right)\left(2\times 2x^{2-1}-11x^{1-1}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(2x^{2}-11x^{1}+15\right)\left(-5\right)x^{0}-\left(-5x^{1}+11\right)\left(4x^{1}-11x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Whakareatia 2x^{2}-11x^{1}+15 ki te -5x^{0}.

$$\frac{2x^{2}\left(-5\right)x^{0}-11x^{1}\left(-5\right)x^{0}+15\left(-5\right)x^{0}-\left(-5x^{1}+11\right)\left(4x^{1}-11x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Whakareatia -5x^{1}+11 ki te 4x^{1}-11x^{0}.

$$\frac{2x^{2}\left(-5\right)x^{0}-11x^{1}\left(-5\right)x^{0}+15\left(-5\right)x^{0}-\left(-5x^{1}\times 4x^{1}-5x^{1}\left(-11\right)x^{0}+11\times 4x^{1}+11\left(-11\right)x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

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

$$\frac{2\left(-5\right)x^{2}-11\left(-5\right)x^{1}+15\left(-5\right)x^{0}-\left(-5\times 4x^{1+1}-5\left(-11\right)x^{1}+11\times 4x^{1}+11\left(-11\right)x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Whakarūnātia.

$$\frac{-10x^{2}+55x^{1}-75x^{0}-\left(-20x^{2}+55x^{1}+44x^{1}-121x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{10x^{2}-44x^{1}+46x^{0}}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{10x^{2}-44x+46x^{0}}{\left(2x^{2}-11x+15\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{10x^{2}-44x+46\times 1}{\left(2x^{2}-11x+15\right)^{2}}$$

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

$$\frac{10x^{2}-44x+46}{\left(2x^{2}-11x+15\right)^{2}}$$