Resol (1/1-x-1/1+x)div(x/x^2-1+x)

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

Calcula

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

Passos de solució senzills

Per afegir o restar les expressions, amplieu-les perquè els denominadors coincideixin. El mínim comú múltiple de 1-x i 1+x és \left(x+1\right)\left(-x+1\right). Multipliqueu \frac{1}{1-x} per \frac{x+1}{x+1}. Multipliqueu \frac{1}{1+x} per \frac{-x+1}{-x+1}.

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

Com que \frac{x+1}{\left(x+1\right)\left(-x+1\right)} i \frac{-x+1}{\left(x+1\right)\left(-x+1\right)} tenen el mateix denominador, resteu-los mitjançant la subtracció dels seus numeradors.

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

Feu les multiplicacions a x+1-\left(-x+1\right).

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

Combineu els termes similars de x+1+x-1.

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

Aïlleu la x^{2}-1.

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

Per afegir o restar les expressions, amplieu-les perquè els denominadors coincideixin. Multipliqueu x per \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.

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

Com que \frac{x}{\left(x-1\right)\left(x+1\right)} i \frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} tenen el mateix denominador, afegiu-los mitjançant l'addició dels seus numeradors.

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

Feu les multiplicacions a x+x\left(x-1\right)\left(x+1\right).

$$\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x+x^{3}+x^{2}-x^{2}-x}{\left(x-1\right)\left(x+1\right)}}$$

Combineu els termes similars de x+x^{3}+x^{2}-x^{2}-x.

$$\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}$$

Dividiu \frac{2x}{\left(x+1\right)\left(-x+1\right)} per \frac{x^{3}}{\left(x-1\right)\left(x+1\right)} multiplicant \frac{2x}{\left(x+1\right)\left(-x+1\right)} pel recíproc de \frac{x^{3}}{\left(x-1\right)\left(x+1\right)}.

$$\frac{2x\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(-x+1\right)x^{3}}$$

Extraieu el signe negatiu de x-1.

$$\frac{-2x\left(x+1\right)\left(-x+1\right)}{\left(x+1\right)\left(-x+1\right)x^{3}}$$

Anul·leu x\left(x+1\right)\left(-x+1\right) tant al numerador com al denominador.

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

Expandiu

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

Passos de solució senzills

Per afegir o restar les expressions, amplieu-les perquè els denominadors coincideixin. El mínim comú múltiple de 1-x i 1+x és \left(x+1\right)\left(-x+1\right). Multipliqueu \frac{1}{1-x} per \frac{x+1}{x+1}. Multipliqueu \frac{1}{1+x} per \frac{-x+1}{-x+1}.

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

Com que \frac{x+1}{\left(x+1\right)\left(-x+1\right)} i \frac{-x+1}{\left(x+1\right)\left(-x+1\right)} tenen el mateix denominador, resteu-los mitjançant la subtracció dels seus numeradors.

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

Feu les multiplicacions a x+1-\left(-x+1\right).

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

Combineu els termes similars de x+1+x-1.

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

Aïlleu la x^{2}-1.

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

Per afegir o restar les expressions, amplieu-les perquè els denominadors coincideixin. Multipliqueu x per \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.

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

Com que \frac{x}{\left(x-1\right)\left(x+1\right)} i \frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} tenen el mateix denominador, afegiu-los mitjançant l'addició dels seus numeradors.

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

Feu les multiplicacions a x+x\left(x-1\right)\left(x+1\right).

$$\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x+x^{3}+x^{2}-x^{2}-x}{\left(x-1\right)\left(x+1\right)}}$$

Combineu els termes similars de x+x^{3}+x^{2}-x^{2}-x.

$$\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}$$

Dividiu \frac{2x}{\left(x+1\right)\left(-x+1\right)} per \frac{x^{3}}{\left(x-1\right)\left(x+1\right)} multiplicant \frac{2x}{\left(x+1\right)\left(-x+1\right)} pel recíproc de \frac{x^{3}}{\left(x-1\right)\left(x+1\right)}.

$$\frac{2x\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(-x+1\right)x^{3}}$$

Extraieu el signe negatiu de x-1.

$$\frac{-2x\left(x+1\right)\left(-x+1\right)}{\left(x+1\right)\left(-x+1\right)x^{3}}$$

Anul·leu x\left(x+1\right)\left(-x+1\right) tant al numerador com al denominador.

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