Issolvi 2/x^4-4x^2-1/x^3-x^2-4x+4

$$\frac { 2 } { x ^ { 4 } - 4 x ^ { 2 } } - \frac { 1 } { x ^ { 3 } - x ^ { 2 } - 4 x + 4 }$$

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Iffattura x^{4}-4x^{2}. Iffattura x^{3}-x^{2}-4x+4.

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

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

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

Billi \frac{2\left(x-1\right)}{\left(x-2\right)\left(x-1\right)\left(x+2\right)x^{2}} u \frac{x^{2}}{\left(x-2\right)\left(x-1\right)\left(x+2\right)x^{2}} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi 2\left(x-1\right)-x^{2}.

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

Espandi \left(x-2\right)\left(x-1\right)\left(x+2\right)x^{2}.

$$\frac{2x-2-x^{2}}{x^{5}-x^{4}-4x^{3}+4x^{2}}$$

Iddifferenzja w.r.t. x

$$\frac{3x^{5}-10x^{4}+12x^{3}+8x^{2}-32x+16}{x^{3}\left(\left(x-1\right)\left(x^{2}-4\right)\right)^{2}}$$