Whakaoti i te 2/a-4-3/a-2

$$\frac { 2 } { a - 4 } - \frac { 3 } { a - 2 }$$

Aromātai

$$\frac{8-a}{\left(a-4\right)\left(a-2\right)}$$

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 a-4 me a-2 ko \left(a-4\right)\left(a-2\right). Whakareatia \frac{2}{a-4} ki te \frac{a-2}{a-2}. Whakareatia \frac{3}{a-2} ki te \frac{a-4}{a-4}.

$$\frac{2\left(a-2\right)}{\left(a-4\right)\left(a-2\right)}-\frac{3\left(a-4\right)}{\left(a-4\right)\left(a-2\right)}$$

Tā te mea he rite te tauraro o \frac{2\left(a-2\right)}{\left(a-4\right)\left(a-2\right)} me \frac{3\left(a-4\right)}{\left(a-4\right)\left(a-2\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2\left(a-2\right)-3\left(a-4\right)}{\left(a-4\right)\left(a-2\right)}$$

Mahia ngā whakarea i roto o 2\left(a-2\right)-3\left(a-4\right).

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

Whakakotahitia ngā kupu rite i 2a-4-3a+12.

$$\frac{-a+8}{\left(a-4\right)\left(a-2\right)}$$

Whakarohaina te \left(a-4\right)\left(a-2\right).

$$\frac{-a+8}{a^{2}-6a+8}$$

Kimi Pārōnaki e ai ki a

$$\frac{a^{2}-16a+40}{a^{4}-12a^{3}+52a^{2}-96a+64}$$

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 a-4 me a-2 ko \left(a-4\right)\left(a-2\right). Whakareatia \frac{2}{a-4} ki te \frac{a-2}{a-2}. Whakareatia \frac{3}{a-2} ki te \frac{a-4}{a-4}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2\left(a-2\right)}{\left(a-4\right)\left(a-2\right)}-\frac{3\left(a-4\right)}{\left(a-4\right)\left(a-2\right)})$$

Tā te mea he rite te tauraro o \frac{2\left(a-2\right)}{\left(a-4\right)\left(a-2\right)} me \frac{3\left(a-4\right)}{\left(a-4\right)\left(a-2\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2\left(a-2\right)-3\left(a-4\right)}{\left(a-4\right)\left(a-2\right)})$$

Mahia ngā whakarea i roto o 2\left(a-2\right)-3\left(a-4\right).

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2a-4-3a+12}{\left(a-4\right)\left(a-2\right)})$$

Whakakotahitia ngā kupu rite i 2a-4-3a+12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-a+8}{\left(a-4\right)\left(a-2\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o a-4 ki ia tau o a-2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-a+8}{a^{2}-2a-4a+8})$$

Pahekotia te -2a me -4a, ka -6a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-a+8}{a^{2}-6a+8})$$

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.

$$\frac{\left(a^{2}-6a^{1}+8\right)\frac{\mathrm{d}}{\mathrm{d}a}(-a^{1}+8)-\left(-a^{1}+8\right)\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}-6a^{1}+8)}{\left(a^{2}-6a^{1}+8\right)^{2}}$$

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}.

$$\frac{\left(a^{2}-6a^{1}+8\right)\left(-1\right)a^{1-1}-\left(-a^{1}+8\right)\left(2a^{2-1}-6a^{1-1}\right)}{\left(a^{2}-6a^{1}+8\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(a^{2}-6a^{1}+8\right)\left(-1\right)a^{0}-\left(-a^{1}+8\right)\left(2a^{1}-6a^{0}\right)}{\left(a^{2}-6a^{1}+8\right)^{2}}$$

Whakareatia a^{2}-6a^{1}+8 ki te -a^{0}.

$$\frac{a^{2}\left(-1\right)a^{0}-6a^{1}\left(-1\right)a^{0}+8\left(-1\right)a^{0}-\left(-a^{1}+8\right)\left(2a^{1}-6a^{0}\right)}{\left(a^{2}-6a^{1}+8\right)^{2}}$$

Whakareatia -a^{1}+8 ki te 2a^{1}-6a^{0}.

$$\frac{a^{2}\left(-1\right)a^{0}-6a^{1}\left(-1\right)a^{0}+8\left(-1\right)a^{0}-\left(-a^{1}\times 2a^{1}-a^{1}\left(-6\right)a^{0}+8\times 2a^{1}+8\left(-6\right)a^{0}\right)}{\left(a^{2}-6a^{1}+8\right)^{2}}$$

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

$$\frac{-a^{2}-6\left(-1\right)a^{1}+8\left(-1\right)a^{0}-\left(-2a^{1+1}-\left(-6a^{1}\right)+8\times 2a^{1}+8\left(-6\right)a^{0}\right)}{\left(a^{2}-6a^{1}+8\right)^{2}}$$

Whakarūnātia.

$$\frac{-a^{2}+6a^{1}-8a^{0}-\left(-2a^{2}+6a^{1}+16a^{1}-48a^{0}\right)}{\left(a^{2}-6a^{1}+8\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{a^{2}-16a^{1}+40a^{0}}{\left(a^{2}-6a^{1}+8\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{a^{2}-16a+40a^{0}}{\left(a^{2}-6a+8\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{a^{2}-16a+40\times 1}{\left(a^{2}-6a+8\right)^{2}}$$

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

$$\frac{a^{2}-16a+40}{\left(a^{2}-6a+8\right)^{2}}$$