Whakaoti i te 2x/1+1{1+frac{x/1-x}}=

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

Aromātai

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

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{1-x}{1-x}.

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

Tā te mea he rite te tauraro o \frac{1-x}{1-x} me \frac{x}{1-x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Whakakotahitia ngā kupu rite i 1-x+x.

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

Whakawehe 1 ki te \frac{1}{1-x} mā te whakarea 1 ki te tau huripoki o \frac{1}{1-x}.

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

Tāpirihia te 1 ki te 1, ka 2.

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

Kimi Pārōnaki e ai ki x

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

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. Whakareatia 1 ki te \frac{1-x}{1-x}.

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

Tā te mea he rite te tauraro o \frac{1-x}{1-x} me \frac{x}{1-x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Whakakotahitia ngā kupu rite i 1-x+x.

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

Whakawehe 1 ki te \frac{1}{1-x} mā te whakarea 1 ki te tau huripoki o \frac{1}{1-x}.

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

Tāpirihia te 1 ki te 1, ka 2.

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

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.

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

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}.

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

Mahia ngā tātaitanga.

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

Whakarohaina mā te āhuatanga tohatoha.

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

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

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

Mahia ngā tātaitanga.

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

Pahekotia ngā kīanga tau ōrite.

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

Tango -2 mai i -2.

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

Mō tētahi kupu t, t^{1}=t.

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

Mō tētahi kupu t mahue te 0, t^{0}=1.

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

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

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