Issolvi (x-2/x^2+2x-x-1/x^2+4x+4/frac{4-x{x}})

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

Evalwa

$$\frac{-2x^{3}+5x^{2}+4x-16}{x\left(4-x\right)\left(x+2\right)^{2}}$$

Passi Qosra tas-Soluzzjonijiet

Iddividi \frac{x-1}{x^{2}+4x+4} b'\frac{4-x}{x} billi timmultiplika \frac{x-1}{x^{2}+4x+4} bir-reċiproku ta' \frac{4-x}{x}.

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

Iffattura x^{2}+2x. Iffattura \left(x^{2}+4x+4\right)\left(4-x\right).

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

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 \left(-x+4\right)\left(x+2\right)^{2} huwa x\left(x-4\right)\left(x+2\right)^{2}. Immultiplika \frac{x-2}{x\left(x+2\right)} b'\frac{\left(x-4\right)\left(x+2\right)}{\left(x-4\right)\left(x+2\right)}. Immultiplika \frac{\left(x-1\right)x}{\left(-x+4\right)\left(x+2\right)^{2}} b'\frac{-x}{-x}.

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

Billi \frac{\left(x-2\right)\left(x-4\right)\left(x+2\right)}{x\left(x-4\right)\left(x+2\right)^{2}} u \frac{\left(x-1\right)x\left(-1\right)x}{x\left(x-4\right)\left(x+2\right)^{2}} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi \left(x-2\right)\left(x-4\right)\left(x+2\right)-\left(x-1\right)x\left(-1\right)x.

$$\frac{x^{3}-2x^{2}-8x-2x^{2}+4x+16+x^{3}-x^{2}}{x\left(x-4\right)\left(x+2\right)^{2}}$$

Ikkombina termini simili f'x^{3}-2x^{2}-8x-2x^{2}+4x+16+x^{3}-x^{2}.

$$\frac{2x^{3}-5x^{2}-4x+16}{x\left(x-4\right)\left(x+2\right)^{2}}$$

Espandi x\left(x-4\right)\left(x+2\right)^{2}.

$$\frac{2x^{3}-5x^{2}-4x+16}{x^{4}-12x^{2}-16x}$$

Espandi

$$\frac{-2x^{3}+5x^{2}+4x-16}{x\left(4-x\right)\left(x+2\right)^{2}}$$

Passi Qosra tas-Soluzzjonijiet

Iddividi \frac{x-1}{x^{2}+4x+4} b'\frac{4-x}{x} billi timmultiplika \frac{x-1}{x^{2}+4x+4} bir-reċiproku ta' \frac{4-x}{x}.

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

Iffattura x^{2}+2x. Iffattura \left(x^{2}+4x+4\right)\left(4-x\right).

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

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 \left(-x+4\right)\left(x+2\right)^{2} huwa x\left(x-4\right)\left(x+2\right)^{2}. Immultiplika \frac{x-2}{x\left(x+2\right)} b'\frac{\left(x-4\right)\left(x+2\right)}{\left(x-4\right)\left(x+2\right)}. Immultiplika \frac{\left(x-1\right)x}{\left(-x+4\right)\left(x+2\right)^{2}} b'\frac{-x}{-x}.

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

Billi \frac{\left(x-2\right)\left(x-4\right)\left(x+2\right)}{x\left(x-4\right)\left(x+2\right)^{2}} u \frac{\left(x-1\right)x\left(-1\right)x}{x\left(x-4\right)\left(x+2\right)^{2}} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi \left(x-2\right)\left(x-4\right)\left(x+2\right)-\left(x-1\right)x\left(-1\right)x.

$$\frac{x^{3}-2x^{2}-8x-2x^{2}+4x+16+x^{3}-x^{2}}{x\left(x-4\right)\left(x+2\right)^{2}}$$

Ikkombina termini simili f'x^{3}-2x^{2}-8x-2x^{2}+4x+16+x^{3}-x^{2}.

$$\frac{2x^{3}-5x^{2}-4x+16}{x\left(x-4\right)\left(x+2\right)^{2}}$$

Espandi x\left(x-4\right)\left(x+2\right)^{2}.

$$\frac{2x^{3}-5x^{2}-4x+16}{x^{4}-12x^{2}-16x}$$