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

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

Aromātai

$$\frac{x+7}{\left(2x-1\right)\left(x+2\right)}$$

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

$$\frac{3\left(x+2\right)}{\left(2x-1\right)\left(x+2\right)}-\frac{2x-1}{\left(2x-1\right)\left(x+2\right)}$$

Tā te mea he rite te tauraro o \frac{3\left(x+2\right)}{\left(2x-1\right)\left(x+2\right)} me \frac{2x-1}{\left(2x-1\right)\left(x+2\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3\left(x+2\right)-\left(2x-1\right)}{\left(2x-1\right)\left(x+2\right)}$$

Mahia ngā whakarea i roto o 3\left(x+2\right)-\left(2x-1\right).

$$\frac{3x+6-2x+1}{\left(2x-1\right)\left(x+2\right)}$$

Whakakotahitia ngā kupu rite i 3x+6-2x+1.

$$\frac{x+7}{\left(2x-1\right)\left(x+2\right)}$$

Whakarohaina te \left(2x-1\right)\left(x+2\right).

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

Kimi Pārōnaki e ai ki x

$$-\frac{2x^{2}+28x+23}{4x^{4}+12x^{3}+x^{2}-12x+4}$$

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

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

Tā te mea he rite te tauraro o \frac{3\left(x+2\right)}{\left(2x-1\right)\left(x+2\right)} me \frac{2x-1}{\left(2x-1\right)\left(x+2\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 3\left(x+2\right)-\left(2x-1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+6-2x+1}{\left(2x-1\right)\left(x+2\right)})$$

Whakakotahitia ngā kupu rite i 3x+6-2x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+7}{\left(2x-1\right)\left(x+2\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2x-1 ki ia tau o x+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+7}{2x^{2}+4x-x-2})$$

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

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

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.

$$\frac{\left(2x^{2}+3x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+7)-\left(x^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+3x^{1}-2)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

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}.

$$\frac{\left(2x^{2}+3x^{1}-2\right)x^{1-1}-\left(x^{1}+7\right)\left(2\times 2x^{2-1}+3x^{1-1}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(2x^{2}+3x^{1}-2\right)x^{0}-\left(x^{1}+7\right)\left(4x^{1}+3x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

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

$$\frac{2x^{2}x^{0}+3x^{1}x^{0}-2x^{0}-\left(x^{1}+7\right)\left(4x^{1}+3x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

Whakareatia x^{1}+7 ki te 4x^{1}+3x^{0}.

$$\frac{2x^{2}x^{0}+3x^{1}x^{0}-2x^{0}-\left(x^{1}\times 4x^{1}+x^{1}\times 3x^{0}+7\times 4x^{1}+7\times 3x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

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

$$\frac{2x^{2}+3x^{1}-2x^{0}-\left(4x^{1+1}+3x^{1}+7\times 4x^{1}+7\times 3x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

Whakarūnātia.

$$\frac{2x^{2}+3x^{1}-2x^{0}-\left(4x^{2}+3x^{1}+28x^{1}+21x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-2x^{2}-28x^{1}-23x^{0}}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-2x^{2}-28x-23x^{0}}{\left(2x^{2}+3x-2\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-2x^{2}-28x-23}{\left(2x^{2}+3x-2\right)^{2}}$$