Whakaoti i te a^5/a-1-a^2/a+1-1/a-1+1/a+1

$$\frac { a ^ { 5 } } { a - 1 } - \frac { a ^ { 2 } } { a + 1 } - \frac { 1 } { a - 1 } + \frac { 1 } { a + 1 }$$

Aromātai

$$a^{4}+a^{3}+a^{2}+2$$

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-1 me a+1 ko \left(a-1\right)\left(a+1\right). Whakareatia \frac{a^{5}}{a-1} ki te \frac{a+1}{a+1}. Whakareatia \frac{a^{2}}{a+1} ki te \frac{a-1}{a-1}.

$$\frac{a^{5}\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1}$$

Tā te mea he rite te tauraro o \frac{a^{5}\left(a+1\right)}{\left(a-1\right)\left(a+1\right)} me \frac{a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{a^{5}\left(a+1\right)-a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1}$$

Mahia ngā whakarea i roto o a^{5}\left(a+1\right)-a^{2}\left(a-1\right).

$$\frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(a-1\right)\left(a+1\right) me a-1 ko \left(a-1\right)\left(a+1\right). Whakareatia \frac{1}{a-1} ki te \frac{a+1}{a+1}.

$$\frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)}-\frac{a+1}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1}$$

Tā te mea he rite te tauraro o \frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)} me \frac{a+1}{\left(a-1\right)\left(a+1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1}$$

Mahia ngā whakarea i roto o a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right).

$$\frac{a^{6}+a^{5}-a^{3}+a^{2}-a-1}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{a^{6}+a^{5}-a^{3}+a^{2}-a-1}{\left(a-1\right)\left(a+1\right)}.

$$\frac{\left(a-1\right)\left(a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1\right)}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1}$$

Me whakakore tahi te a-1 i te taurunga me te tauraro.

$$\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1}+\frac{1}{a+1}$$

Tā te mea he rite te tauraro o \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1} me \frac{1}{a+1}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1}{a+1}$$

Whakakotahitia ngā kupu rite i a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1.

$$\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1}.

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

Me whakakore tahi te a+1 i te taurunga me te tauraro.

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

Me whakaroha te kīanga.

$$a^{4}+a^{3}+a^{2}+2$$

Kimi Pārōnaki e ai ki a

$$a\left(4a^{2}+3a+2\right)$$

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o a-1 me a+1 ko \left(a-1\right)\left(a+1\right). Whakareatia \frac{a^{5}}{a-1} ki te \frac{a+1}{a+1}. Whakareatia \frac{a^{2}}{a+1} ki te \frac{a-1}{a-1}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1})$$

Tā te mea he rite te tauraro o \frac{a^{5}\left(a+1\right)}{\left(a-1\right)\left(a+1\right)} me \frac{a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}\left(a+1\right)-a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1})$$

Mahia ngā whakarea i roto o a^{5}\left(a+1\right)-a^{2}\left(a-1\right).

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(a-1\right)\left(a+1\right) me a-1 ko \left(a-1\right)\left(a+1\right). Whakareatia \frac{1}{a-1} ki te \frac{a+1}{a+1}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)}-\frac{a+1}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1})$$

Tā te mea he rite te tauraro o \frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)} me \frac{a+1}{\left(a-1\right)\left(a+1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1})$$

Mahia ngā whakarea i roto o a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right).

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{6}+a^{5}-a^{3}+a^{2}-a-1}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1})$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{a^{6}+a^{5}-a^{3}+a^{2}-a-1}{\left(a-1\right)\left(a+1\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\left(a-1\right)\left(a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1\right)}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1})$$

Me whakakore tahi te a-1 i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1}+\frac{1}{a+1})$$

Tā te mea he rite te tauraro o \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1} me \frac{1}{a+1}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1}{a+1})$$

Whakakotahitia ngā kupu rite i a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1})$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1}.

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

Me whakakore tahi te a+1 i te taurunga me te tauraro.

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

Me whakaroha te kīanga.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}+a^{3}+a^{2}+2)$$

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}.

$$4a^{4-1}+3a^{3-1}+2a^{2-1}$$

Tango 1 mai i 4.

$$4a^{3}+3a^{3-1}+2a^{2-1}$$

Tango 1 mai i 3.

$$4a^{3}+3a^{2}+2a^{2-1}$$

Tango 1 mai i 2.

$$4a^{3}+3a^{2}+2a^{1}$$

Mō tētahi kupu t, t^{1}=t.

$$4a^{3}+3a^{2}+2a$$