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

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

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

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

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

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

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

Billi \frac{x-1}{x\left(x-1\right)\left(x+1\right)} u \frac{x+1}{x\left(x-1\right)\left(x+1\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Ikkombina termini simili f'x-1+x+1.

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

Annulla x fin-numeratur u d-denominatur.

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

Espandi \left(x-1\right)\left(x+1\right).

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

Iddifferenzja w.r.t. x

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