Whakaoti i te x/frac{4{x^2}-1}=

$$\frac { x } { \frac { 4 } { x ^ { 2 } } - 1 } =$$

Aromātai

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

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{x^{2}}{x^{2}}.

$$\frac{x}{\frac{4}{x^{2}}-\frac{x^{2}}{x^{2}}}$$

Tā te mea he rite te tauraro o \frac{4}{x^{2}} me \frac{x^{2}}{x^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x}{\frac{4-x^{2}}{x^{2}}}$$

Whakawehe x ki te \frac{4-x^{2}}{x^{2}} mā te whakarea x ki te tau huripoki o \frac{4-x^{2}}{x^{2}}.

$$\frac{xx^{2}}{4-x^{2}}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

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

Kimi Pārōnaki e ai ki x

$$\left(\frac{x}{x^{2}-4}\right)^{2}\left(12-x^{2}\right)$$

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{x^{2}}{x^{2}}.

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

Tā te mea he rite te tauraro o \frac{4}{x^{2}} me \frac{x^{2}}{x^{2}}, me tango rāua mā te tango i ō raua taurunga.

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

Whakawehe x ki te \frac{4-x^{2}}{x^{2}} mā te whakarea x ki te tau huripoki o \frac{4-x^{2}}{x^{2}}.

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

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{4-x^{2}})$$

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.

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

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}.

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

Mahia ngā tātaitanga.

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

Whakarohaina mā te āhuatanga tohatoha.

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

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

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

Mahia ngā tātaitanga.

$$\frac{-3x^{4}+12x^{2}-\left(-2x^{4}\right)}{\left(-x^{2}+4\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(-3-\left(-2\right)\right)x^{4}+12x^{2}}{\left(-x^{2}+4\right)^{2}}$$

Tango -2 mai i -3.

$$\frac{-x^{4}+12x^{2}}{\left(-x^{2}+4\right)^{2}}$$

Tauwehea te x^{2}.

$$\frac{x^{2}\left(-x^{2}+12x^{0}\right)}{\left(-x^{2}+4\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{x^{2}\left(-x^{2}+12\times 1\right)}{\left(-x^{2}+4\right)^{2}}$$

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

$$\frac{x^{2}\left(-x^{2}+12\right)}{\left(-x^{2}+4\right)^{2}}$$