Réitigh 2y-6/y^2-9-y/y-1+y^2+2/y^2+2y-3

$$\frac { 2 y - 6 } { y ^ { 2 } - 9 } - \frac { y } { y - 1 } + \frac { y ^ { 2 } + 2 } { y ^ { 2 } + 2 y - 3 }$$

Luacháil

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

Céimeanna gearra réitigh

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{2y-6}{y^{2}-9}.

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

Cealaigh y-3 mar uimhreoir agus ainmneoir.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de y+3 agus y-1 ná \left(y-1\right)\left(y+3\right). Méadaigh \frac{2}{y+3} faoi \frac{y-1}{y-1}. Méadaigh \frac{y}{y-1} faoi \frac{y+3}{y+3}.

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

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

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

Déan iolrúcháin in 2\left(y-1\right)-y\left(y+3\right).

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

Cumaisc téarmaí comhchosúla in: 2y-2-y^{2}-3y.

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

Fachtóirigh y^{2}+2y-3.

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

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

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

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

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

Fairsingigh \left(y-1\right)\left(y+3\right)

$$\frac{-y}{y^{2}+2y-3}$$

Fairsingigh

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

Céimeanna gearra réitigh

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{2y-6}{y^{2}-9}.

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

Cealaigh y-3 mar uimhreoir agus ainmneoir.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de y+3 agus y-1 ná \left(y-1\right)\left(y+3\right). Méadaigh \frac{2}{y+3} faoi \frac{y-1}{y-1}. Méadaigh \frac{y}{y-1} faoi \frac{y+3}{y+3}.

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

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

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

Déan iolrúcháin in 2\left(y-1\right)-y\left(y+3\right).

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

Cumaisc téarmaí comhchosúla in: 2y-2-y^{2}-3y.

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

Fachtóirigh y^{2}+2y-3.

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

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

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

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

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

Fairsingigh \left(y-1\right)\left(y+3\right)

$$\frac{-y}{y^{2}+2y-3}$$