Issolvi (1/1+x+2x/1-x^2)*(1/x-1)

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

Evalwa

$$\frac{1}{x}$$

Passi Qosra tas-Soluzzjonijiet

Iffattura 1-x^{2}.

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

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

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

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

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

Ikkombina termini simili f'x-1-2x.

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

Estratta l-sinjal negattiv fi -x-1.

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

Annulla x+1 fin-numeratur u d-denominatur.

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 1 b'\frac{x}{x}.

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

Billi \frac{1}{x} u \frac{x}{x} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{-1}{x-1}\times \frac{1-x}{x}$$

Immultiplika \frac{-1}{x-1} b'\frac{1-x}{x} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Estratta l-sinjal negattiv fi 1-x.

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

Annulla x-1 fin-numeratur u d-denominatur.

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

Immultiplika -1 u -1 biex tikseb 1.

$$\frac{1}{x}$$

Espandi

$$\frac{1}{x}$$

Passi Qosra tas-Soluzzjonijiet

Iffattura 1-x^{2}.

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

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

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

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

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

Ikkombina termini simili f'x-1-2x.

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

Estratta l-sinjal negattiv fi -x-1.

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

Annulla x+1 fin-numeratur u d-denominatur.

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 1 b'\frac{x}{x}.

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

Billi \frac{1}{x} u \frac{x}{x} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{-1}{x-1}\times \frac{1-x}{x}$$

Immultiplika \frac{-1}{x-1} b'\frac{1-x}{x} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Estratta l-sinjal negattiv fi 1-x.

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

Annulla x-1 fin-numeratur u d-denominatur.

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

Immultiplika -1 u -1 biex tikseb 1.

$$\frac{1}{x}$$