Réitigh S1/x^2-2x-1/x^2+2x

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

Luacháil

$$\frac{Sx-x+2S+2}{x\left(x^{2}-4\right)}$$

$$x\neq 0\text{ and }|x|\neq 2$$

Céimeanna gearra réitigh

Scríobh S\times \frac{1}{x^{2}-2x} mar chodán aonair.

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

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

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

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

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

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

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

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

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

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

$$\frac{Sx+2S-x+2}{x^{3}-4x}$$

Difreálaigh w.r.t. x

$$\frac{2\left(4+4S-3x^{2}-3Sx^{2}+x^{3}-Sx^{3}\right)}{\left(x\left(x^{2}-4\right)\right)^{2}}$$

$$x\neq 0\text{ and }|x|\neq 2$$