Whakaoti i te 1/x+21/2-x

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

Aromātai

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

Ngā Hipanga Rongoā Poto

Tuhia te 2\times \frac{1}{2-x} hei hautanga kotahi.

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

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

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

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

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

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

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

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

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

Kimi Pārōnaki e ai ki x

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

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

Tuhia te 2\times \frac{1}{2-x} hei hautanga kotahi.

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

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

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

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

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

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

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

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

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

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.

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

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}.

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

Whakarūnātia.

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

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

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

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

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

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

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

Whakarūnātia.

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

Pahekotia ngā kīanga tau ōrite.

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

Mō tētahi kupu t, t^{1}=t.

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

Mō tētahi kupu t mahue te 0, t^{0}=1.

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