Réitigh 1/x^2-5x+6+1/x^2-3x+2+2/x^2-8x+15

$$\frac { 1 } { x ^ { 2 } - 5 x + 6 } + \frac { 1 } { x ^ { 2 } - 3 x + 2 } + \frac { 2 } { x ^ { 2 } - 8 x + 15 }$$

Luacháil

$$\frac{4}{\left(x-5\right)\left(x-1\right)}$$

Céimeanna gearra réitigh

Fachtóirigh x^{2}-5x+6. Fachtóirigh x^{2}-3x+2.

$$\frac{1}{\left(x-3\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

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

$$\frac{x-1}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

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

$$\frac{x-1+x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Cumaisc téarmaí comhchosúla in: x-1+x-3.

$$\frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}.

$$\frac{2\left(x-2\right)}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Cealaigh x-2 mar uimhreoir agus ainmneoir.

$$\frac{2}{\left(x-3\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Fachtóirigh x^{2}-8x+15.

$$\frac{2}{\left(x-3\right)\left(x-1\right)}+\frac{2}{\left(x-5\right)\left(x-3\right)}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-3\right)\left(x-1\right) agus \left(x-5\right)\left(x-3\right) ná \left(x-5\right)\left(x-3\right)\left(x-1\right). Méadaigh \frac{2}{\left(x-3\right)\left(x-1\right)} faoi \frac{x-5}{x-5}. Méadaigh \frac{2}{\left(x-5\right)\left(x-3\right)} faoi \frac{x-1}{x-1}.

$$\frac{2\left(x-5\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}+\frac{2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

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

$$\frac{2\left(x-5\right)+2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Déan iolrúcháin in 2\left(x-5\right)+2\left(x-1\right).

$$\frac{2x-10+2x-2}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Cumaisc téarmaí comhchosúla in: 2x-10+2x-2.

$$\frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}.

$$\frac{4\left(x-3\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Cealaigh x-3 mar uimhreoir agus ainmneoir.

$$\frac{4}{\left(x-5\right)\left(x-1\right)}$$

Fairsingigh \left(x-5\right)\left(x-1\right)

$$\frac{4}{x^{2}-6x+5}$$

Difreálaigh w.r.t. x

$$\frac{8\left(3-x\right)}{\left(\left(x-5\right)\left(x-1\right)\right)^{2}}$$