Réitigh 1/x^2+x-1/x^2-1

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

Luacháil

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

Céimeanna gearra réitigh

Fachtóirigh x^{2}+x. Fachtóirigh x^{2}-1.

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

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

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

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

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

Cumaisc téarmaí comhchosúla in: x-1-x.

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

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

$$\frac{-1}{x^{3}-x}$$

Difreálaigh w.r.t. x

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