Réitigh 2/x^2+7x+10+3/x^2-25

$$\frac { 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 } { x ^ { 2 } - 25 }$$

Luacháil

$$\frac{5x-4}{\left(x+2\right)\left(x^{2}-25\right)}$$

Céimeanna gearra réitigh

Fachtóirigh x^{2}+7x+10. Fachtóirigh x^{2}-25.

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

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+2\right)\left(x+5\right) agus \left(x-5\right)\left(x+5\right) ná \left(x-5\right)\left(x+2\right)\left(x+5\right). Méadaigh \frac{2}{\left(x+2\right)\left(x+5\right)} faoi \frac{x-5}{x-5}. Méadaigh \frac{3}{\left(x-5\right)\left(x+5\right)} faoi \frac{x+2}{x+2}.

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

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

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

Déan iolrúcháin in 2\left(x-5\right)+3\left(x+2\right).

$$\frac{2x-10+3x+6}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Cumaisc téarmaí comhchosúla in: 2x-10+3x+6.

$$\frac{5x-4}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Fairsingigh \left(x-5\right)\left(x+2\right)\left(x+5\right)

$$\frac{5x-4}{x^{3}+2x^{2}-25x-50}$$

Difreálaigh w.r.t. x

$$\frac{2\left(-5x^{3}+x^{2}+8x-175\right)}{\left(\left(x+2\right)\left(x^{2}-25\right)\right)^{2}}$$