Réitigh x/x-3+x+1/x^2+9+2/x^2-6x+9

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

Luacháil

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

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 x-3 agus x^{2}+9 ná \left(x-3\right)\left(x^{2}+9\right). Méadaigh \frac{x}{x-3} faoi \frac{x^{2}+9}{x^{2}+9}. Méadaigh \frac{x+1}{x^{2}+9} faoi \frac{x-3}{x-3}.

$$\frac{x\left(x^{2}+9\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Tá an t-ainmneoir céanna ag \frac{x\left(x^{2}+9\right)}{\left(x-3\right)\left(x^{2}+9\right)} agus \frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{x\left(x^{2}+9\right)+\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Déan iolrúcháin in x\left(x^{2}+9\right)+\left(x+1\right)\left(x-3\right).

$$\frac{x^{3}+9x+x^{2}-3x+x-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Cumaisc téarmaí comhchosúla in: x^{3}+9x+x^{2}-3x+x-3.

$$\frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Fachtóirigh x^{2}-6x+9.

$$\frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{\left(x-3\right)^{2}}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-3\right)\left(x^{2}+9\right) agus \left(x-3\right)^{2} ná \left(x-3\right)^{2}\left(x^{2}+9\right). Méadaigh \frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)} faoi \frac{x-3}{x-3}. Méadaigh \frac{2}{\left(x-3\right)^{2}} faoi \frac{x^{2}+9}{x^{2}+9}.

$$\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}+\frac{2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Tá an t-ainmneoir céanna ag \frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)} agus \frac{2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)+2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Déan iolrúcháin in \left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)+2\left(x^{2}+9\right).

$$\frac{x^{4}-3x^{3}+7x^{2}-21x+x^{3}-3x^{2}-3x+9+2x^{2}+18}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Cumaisc téarmaí comhchosúla in: x^{4}-3x^{3}+7x^{2}-21x+x^{3}-3x^{2}-3x+9+2x^{2}+18.

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Fairsingigh \left(x-3\right)^{2}\left(x^{2}+9\right)

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{x^{4}-6x^{3}+18x^{2}-54x+81}$$

Fairsingigh

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

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 x-3 agus x^{2}+9 ná \left(x-3\right)\left(x^{2}+9\right). Méadaigh \frac{x}{x-3} faoi \frac{x^{2}+9}{x^{2}+9}. Méadaigh \frac{x+1}{x^{2}+9} faoi \frac{x-3}{x-3}.

$$\frac{x\left(x^{2}+9\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Tá an t-ainmneoir céanna ag \frac{x\left(x^{2}+9\right)}{\left(x-3\right)\left(x^{2}+9\right)} agus \frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{x\left(x^{2}+9\right)+\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Déan iolrúcháin in x\left(x^{2}+9\right)+\left(x+1\right)\left(x-3\right).

$$\frac{x^{3}+9x+x^{2}-3x+x-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Cumaisc téarmaí comhchosúla in: x^{3}+9x+x^{2}-3x+x-3.

$$\frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Fachtóirigh x^{2}-6x+9.

$$\frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{\left(x-3\right)^{2}}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-3\right)\left(x^{2}+9\right) agus \left(x-3\right)^{2} ná \left(x-3\right)^{2}\left(x^{2}+9\right). Méadaigh \frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)} faoi \frac{x-3}{x-3}. Méadaigh \frac{2}{\left(x-3\right)^{2}} faoi \frac{x^{2}+9}{x^{2}+9}.

$$\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}+\frac{2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Tá an t-ainmneoir céanna ag \frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)} agus \frac{2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)+2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Déan iolrúcháin in \left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)+2\left(x^{2}+9\right).

$$\frac{x^{4}-3x^{3}+7x^{2}-21x+x^{3}-3x^{2}-3x+9+2x^{2}+18}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Cumaisc téarmaí comhchosúla in: x^{4}-3x^{3}+7x^{2}-21x+x^{3}-3x^{2}-3x+9+2x^{2}+18.

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Fairsingigh \left(x-3\right)^{2}\left(x^{2}+9\right)

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{x^{4}-6x^{3}+18x^{2}-54x+81}$$