Whakaoti i te 1/x^2-2x-1/x

$$\frac { 1 } { x ^ { 2 } - 2 x } - \frac { 1 } { x }$$

Aromātai

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

Ngā Hipanga Rongoā Poto

Tauwehea te x^{2}-2x.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o x\left(x-2\right) me x ko x\left(x-2\right). Whakareatia \frac{1}{x} ki te \frac{x-2}{x-2}.

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

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

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

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

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

Whakakotahitia ngā kupu rite i 1-x+2.

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

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

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

Kimi Pārōnaki e ai ki x

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

Ngā Upane e Whakamahi ana i te Ture Pārōnaki mō te Otinga

Tauwehea te x^{2}-2x.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o x\left(x-2\right) me x ko x\left(x-2\right). Whakareatia \frac{1}{x} ki te \frac{x-2}{x-2}.

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

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

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

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

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

Whakakotahitia ngā kupu rite i 1-x+2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-2.

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

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.

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

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}.

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

Whakarūnātia.

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

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

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

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

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

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

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

Whakarūnātia.

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

Pahekotia ngā kīanga tau ōrite.

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

Mō tētahi kupu t, t^{1}=t.

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

Mō tētahi kupu t mahue te 0, t^{0}=1.

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

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

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