Réitigh a+1/a^2-a-a-1/a^2+a-1/a^2-1

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

Luacháil

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

Céimeanna gearra réitigh

Fachtóirigh a^{2}-a. Fachtóirigh a^{2}+a.

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

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

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

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

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

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

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

Cumaisc téarmaí comhchosúla in: a^{2}+a+a+1-a^{2}+a+a-1.

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

Cealaigh a mar uimhreoir agus ainmneoir.

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

Fachtóirigh a^{2}-1.

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

Tá an t-ainmneoir céanna ag \frac{4}{\left(a-1\right)\left(a+1\right)} agus \frac{1}{\left(a-1\right)\left(a+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú. Dealaigh 1 ó 4 chun 3 a fháil.

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

Fairsingigh \left(a-1\right)\left(a+1\right)

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

Fairsingigh

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

Céimeanna gearra réitigh

Fachtóirigh a^{2}-a. Fachtóirigh a^{2}+a.

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

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

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

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

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

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

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

Cumaisc téarmaí comhchosúla in: a^{2}+a+a+1-a^{2}+a+a-1.

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

Cealaigh a mar uimhreoir agus ainmneoir.

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

Fachtóirigh a^{2}-1.

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

Tá an t-ainmneoir céanna ag \frac{4}{\left(a-1\right)\left(a+1\right)} agus \frac{1}{\left(a-1\right)\left(a+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú. Dealaigh 1 ó 4 chun 3 a fháil.

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

Fairsingigh \left(a-1\right)\left(a+1\right)

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