Whakaoti i te 4/x+4-x/x-4

$$\frac { 4 } { x + 4 } - \frac { x } { x - 4 }$$

Aromātai

$$-\frac{x^{2}+16}{x^{2}-16}$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o x+4 me x-4 ko \left(x-4\right)\left(x+4\right). Whakareatia \frac{4}{x+4} ki te \frac{x-4}{x-4}. Whakareatia \frac{x}{x-4} ki te \frac{x+4}{x+4}.

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

Tā te mea he rite te tauraro o \frac{4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)} me \frac{x\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 4\left(x-4\right)-x\left(x+4\right).

$$\frac{4x-16-x^{2}-4x}{\left(x-4\right)\left(x+4\right)}$$

Whakakotahitia ngā kupu rite i 4x-16-x^{2}-4x.

$$\frac{-16-x^{2}}{\left(x-4\right)\left(x+4\right)}$$

Whakarohaina te \left(x-4\right)\left(x+4\right).

$$\frac{-16-x^{2}}{x^{2}-16}$$

Kimi Pārōnaki e ai ki x

$$\frac{64x}{\left(x^{2}-16\right)^{2}}$$

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. Ko te taurea pātahi iti rawa o x+4 me x-4 ko \left(x-4\right)\left(x+4\right). Whakareatia \frac{4}{x+4} ki te \frac{x-4}{x-4}. Whakareatia \frac{x}{x-4} ki te \frac{x+4}{x+4}.

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

Tā te mea he rite te tauraro o \frac{4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)} me \frac{x\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 4\left(x-4\right)-x\left(x+4\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x-16-x^{2}-4x}{\left(x-4\right)\left(x+4\right)})$$

Whakakotahitia ngā kupu rite i 4x-16-x^{2}-4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-16-x^{2}}{\left(x-4\right)\left(x+4\right)})$$

Whakaarohia te \left(x-4\right)\left(x+4\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-16-x^{2}}{x^{2}-4^{2}})$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-16-x^{2}}{x^{2}-16})$$

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.

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

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}.

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

Mahia ngā tātaitanga.

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

Whakarohaina mā te āhuatanga tohatoha.

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

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

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

Mahia ngā tātaitanga.

$$\frac{-2x^{3}+32x^{1}-\left(-2x^{3}-32x^{1}\right)}{\left(x^{2}-16\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{-2x^{3}+32x^{1}-\left(-2x^{3}\right)-\left(-32x^{1}\right)}{\left(x^{2}-16\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(-2-\left(-2\right)\right)x^{3}+\left(32-\left(-32\right)\right)x^{1}}{\left(x^{2}-16\right)^{2}}$$

Tangohia te -2 i -2 me te -32 i te 32.

$$\frac{64x^{1}}{\left(x^{2}-16\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{64x}{\left(x^{2}-16\right)^{2}}$$