Whakaoti i te f(x)=x/x^2-6x-16

$$f ( x ) = \frac { x } { x ^ { 2 } - 6 x - 16 }$$

Kimi Pārōnaki e ai ki x

$$-\frac{x^{2}+16}{\left(\left(x-8\right)\left(x+2\right)\right)^{2}}$$

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

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.

$$\frac{\left(x^{2}-6x^{1}-16\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-6x^{1}-16)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-6x^{1}-16\right)x^{1-1}-x^{1}\left(2x^{2-1}-6x^{1-1}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}-6x^{1}-16\right)x^{0}-x^{1}\left(2x^{1}-6x^{0}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Whakareatia x^{2}-6x^{1}-16 ki te x^{0}.

$$\frac{x^{2}x^{0}-6x^{1}x^{0}-16x^{0}-x^{1}\left(2x^{1}-6x^{0}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Whakareatia x^{1} ki te 2x^{1}-6x^{0}.

$$\frac{x^{2}x^{0}-6x^{1}x^{0}-16x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\left(-6\right)x^{0}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

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

$$\frac{x^{2}-6x^{1}-16x^{0}-\left(2x^{1+1}-6x^{1}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Whakarūnātia.

$$\frac{x^{2}-6x^{1}-16x^{0}-\left(2x^{2}-6x^{1}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-x^{2}-16x^{0}}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-x^{2}-16x^{0}}{\left(x^{2}-6x-16\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-x^{2}-16}{\left(x^{2}-6x-16\right)^{2}}$$

Aromātai

$$\frac{x}{\left(x-8\right)\left(x+2\right)}$$