Réitigh 1/a-1-2/a^2-2a+1/a^2-3a+2

$$\frac { 1 } { a - 1 } - \frac { 2 } { a ^ { 2 } - 2 a } + \frac { 1 } { a ^ { 2 } - 3 a + 2 }$$

Luacháil

$$\frac{1}{a}$$

Céimeanna gearra réitigh

Fachtóirigh a^{2}-2a.

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

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\left(a-2\right) ná a\left(a-2\right)\left(a-1\right). Méadaigh \frac{1}{a-1} faoi \frac{a\left(a-2\right)}{a\left(a-2\right)}. Méadaigh \frac{2}{a\left(a-2\right)} faoi \frac{a-1}{a-1}.

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

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

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

Déan iolrúcháin in a\left(a-2\right)-2\left(a-1\right).

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

Cumaisc téarmaí comhchosúla in: a^{2}-2a-2a+2.

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

Fachtóirigh a^{2}-3a+2.

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

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\left(a-2\right)\left(a-1\right) agus \left(a-2\right)\left(a-1\right) ná a\left(a-2\right)\left(a-1\right). Méadaigh \frac{1}{\left(a-2\right)\left(a-1\right)} faoi \frac{a}{a}.

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

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

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

Cumaisc téarmaí comhchosúla in: a^{2}-4a+2+a.

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

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

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

Cealaigh \left(a-2\right)\left(a-1\right) mar uimhreoir agus ainmneoir.

$$\frac{1}{a}$$

Difreálaigh w.r.t. a

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

Céimeanna ag Baint Úsáid as Sainiú Díorthaigh

Fachtóirigh a^{2}-2a.

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

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\left(a-2\right) ná a\left(a-2\right)\left(a-1\right). Méadaigh \frac{1}{a-1} faoi \frac{a\left(a-2\right)}{a\left(a-2\right)}. Méadaigh \frac{2}{a\left(a-2\right)} faoi \frac{a-1}{a-1}.

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

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

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

Déan iolrúcháin in a\left(a-2\right)-2\left(a-1\right).

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

Cumaisc téarmaí comhchosúla in: a^{2}-2a-2a+2.

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

Fachtóirigh a^{2}-3a+2.

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

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\left(a-2\right)\left(a-1\right) agus \left(a-2\right)\left(a-1\right) ná a\left(a-2\right)\left(a-1\right). Méadaigh \frac{1}{\left(a-2\right)\left(a-1\right)} faoi \frac{a}{a}.

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

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

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

Cumaisc téarmaí comhchosúla in: a^{2}-4a+2+a.

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

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

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

Cealaigh \left(a-2\right)\left(a-1\right) mar uimhreoir agus ainmneoir.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a})$$

Is é díorthach ax^{n} ná nax^{n-1}.

$$-a^{-1-1}$$

Dealaigh 1 ó -1.

$$-a^{-2}$$