Réitigh 1/x^2+4x+3+1/x^2+8x+15+1/x^2+12x+35

$$\frac { 1 } { x ^ { 2 } + 4 x + 3 } + \frac { 1 } { x ^ { 2 } + 8 x + 15 } + \frac { 1 } { x ^ { 2 } + 12 x + 35 }$$

Luacháil

$$\frac{3}{\left(x+1\right)\left(x+7\right)}$$

Céimeanna gearra réitigh

Fachtóirigh x^{2}+4x+3. Fachtóirigh x^{2}+8x+15.

$$\frac{1}{\left(x+1\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

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+1\right)\left(x+3\right) agus \left(x+3\right)\left(x+5\right) ná \left(x+1\right)\left(x+3\right)\left(x+5\right). Méadaigh \frac{1}{\left(x+1\right)\left(x+3\right)} faoi \frac{x+5}{x+5}. Méadaigh \frac{1}{\left(x+3\right)\left(x+5\right)} faoi \frac{x+1}{x+1}.

$$\frac{x+5}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{x+1}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

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

$$\frac{x+5+x+1}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

Cumaisc téarmaí comhchosúla in: x+5+x+1.

$$\frac{2x+6}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{2x+6}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}.

$$\frac{2\left(x+3\right)}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

Cealaigh x+3 mar uimhreoir agus ainmneoir.

$$\frac{2}{\left(x+1\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

Fachtóirigh x^{2}+12x+35.

$$\frac{2}{\left(x+1\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+7\right)}$$

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+1\right)\left(x+5\right) agus \left(x+5\right)\left(x+7\right) ná \left(x+1\right)\left(x+5\right)\left(x+7\right). Méadaigh \frac{2}{\left(x+1\right)\left(x+5\right)} faoi \frac{x+7}{x+7}. Méadaigh \frac{1}{\left(x+5\right)\left(x+7\right)} faoi \frac{x+1}{x+1}.

$$\frac{2\left(x+7\right)}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}+\frac{x+1}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Tá an t-ainmneoir céanna ag \frac{2\left(x+7\right)}{\left(x+1\right)\left(x+5\right)\left(x+7\right)} agus \frac{x+1}{\left(x+1\right)\left(x+5\right)\left(x+7\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{2\left(x+7\right)+x+1}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Déan iolrúcháin in 2\left(x+7\right)+x+1.

$$\frac{2x+14+x+1}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Cumaisc téarmaí comhchosúla in: 2x+14+x+1.

$$\frac{3x+15}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{3x+15}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}.

$$\frac{3\left(x+5\right)}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Cealaigh x+5 mar uimhreoir agus ainmneoir.

$$\frac{3}{\left(x+1\right)\left(x+7\right)}$$

Fairsingigh \left(x+1\right)\left(x+7\right)

$$\frac{3}{x^{2}+8x+7}$$

Difreálaigh w.r.t. x

$$\frac{6\left(-x-4\right)}{\left(\left(x+1\right)\left(x+7\right)\right)^{2}}$$