Réitigh 1/x^2+x+1/x^2-x

$$\frac { 1 } { x ^ { 2 } + x } + \frac { 1 } { x ^ { 2 } - x }$$

Luacháil

$$\frac{2}{x^{2}-1}$$

Céimeanna gearra réitigh

Fachtóirigh x^{2}+x. Fachtóirigh x^{2}-x.

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

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

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

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

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

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

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

Cealaigh x mar uimhreoir agus ainmneoir.

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

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

$$\frac{2}{x^{2}-1}$$

Difreálaigh w.r.t. x

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