Réitigh a^5/a-1-a^2/a+1-1/a-1+1/a+1

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

Luacháil

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

Céimeanna gearra réitigh

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de a-1 agus a+1 ná \left(a-1\right)\left(a+1\right). Méadaigh \frac{a^{5}}{a-1} faoi \frac{a+1}{a+1}. Méadaigh \frac{a^{2}}{a+1} faoi \frac{a-1}{a-1}.

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

Tá an t-ainmneoir céanna ag \frac{a^{5}\left(a+1\right)}{\left(a-1\right)\left(a+1\right)} agus \frac{a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in a^{5}\left(a+1\right)-a^{2}\left(a-1\right).

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(a-1\right)\left(a+1\right) agus a-1 ná \left(a-1\right)\left(a+1\right). Méadaigh \frac{1}{a-1} faoi \frac{a+1}{a+1}.

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

Tá an t-ainmneoir céanna ag \frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)} agus \frac{a+1}{\left(a-1\right)\left(a+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right).

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{a^{6}+a^{5}-a^{3}+a^{2}-a-1}{\left(a-1\right)\left(a+1\right)}.

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

Cealaigh a-1 mar uimhreoir agus ainmneoir.

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

Tá an t-ainmneoir céanna ag \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1} agus \frac{1}{a+1} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

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

Cumaisc téarmaí comhchosúla in: a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1}.

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

Cealaigh a+1 mar uimhreoir agus ainmneoir.

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

Fairsingigh an slonn.

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

Difreálaigh w.r.t. a

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

Céimeanna ag Baint Úsáid as Riail na nDíorthach don tSuim

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de a-1 agus a+1 ná \left(a-1\right)\left(a+1\right). Méadaigh \frac{a^{5}}{a-1} faoi \frac{a+1}{a+1}. Méadaigh \frac{a^{2}}{a+1} faoi \frac{a-1}{a-1}.

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

Tá an t-ainmneoir céanna ag \frac{a^{5}\left(a+1\right)}{\left(a-1\right)\left(a+1\right)} agus \frac{a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in a^{5}\left(a+1\right)-a^{2}\left(a-1\right).

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(a-1\right)\left(a+1\right) agus a-1 ná \left(a-1\right)\left(a+1\right). Méadaigh \frac{1}{a-1} faoi \frac{a+1}{a+1}.

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

Tá an t-ainmneoir céanna ag \frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)} agus \frac{a+1}{\left(a-1\right)\left(a+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right).

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{a^{6}+a^{5}-a^{3}+a^{2}-a-1}{\left(a-1\right)\left(a+1\right)}.

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

Cealaigh a-1 mar uimhreoir agus ainmneoir.

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

Tá an t-ainmneoir céanna ag \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1} agus \frac{1}{a+1} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

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

Cumaisc téarmaí comhchosúla in: a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1}.

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

Cealaigh a+1 mar uimhreoir agus ainmneoir.

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

Fairsingigh an slonn.

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

Is ionann díorthach iltéarmaigh agus suim dhíorthaigh a théarmaí. Is ionann díorthach téarma thairisigh agus 0. Is ionann díorthach ax^{n} agus nax^{n-1}.

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

Dealaigh 1 ó 4.

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

Dealaigh 1 ó 3.

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

Dealaigh 1 ó 2.

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

Do théarma ar bith t, t^{1}=t.

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