Issolvi 1/x^2-2x-1/x^2+2x

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

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

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

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' x\left(x-2\right) u x\left(x+2\right) huwa x\left(x-2\right)\left(x+2\right). Immultiplika \frac{1}{x\left(x-2\right)} b'\frac{x+2}{x+2}. Immultiplika \frac{1}{x\left(x+2\right)} b'\frac{x-2}{x-2}.

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

Billi \frac{x+2}{x\left(x-2\right)\left(x+2\right)} u \frac{x-2}{x\left(x-2\right)\left(x+2\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi x+2-\left(x-2\right).

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

Ikkombina termini simili f'x+2-x+2.

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

Espandi x\left(x-2\right)\left(x+2\right).

$$\frac{4}{x^{3}-4x}$$

Iddifferenzja w.r.t. x

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