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Simplificación de expresiones/ Descomposición en fracciones simples/ ((1/(x-1))-((x+1)/(x^2+x+1)))/(1+(1/(x^3-1)))

¿Cómo vas a descomponer esta ((1/(x-1))-((x+1)/(x^2+x+1)))/(1+(1/(x^3-1))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  1       x + 1   
----- - ----------
x - 1    2        
        x  + x + 1
------------------
          1       
    1 + ------    
         3        
        x  - 1
$$\frac{- \frac{x + 1}{\left(x^{2} + x\right) + 1} + \frac{1}{x - 1}}{1 + \frac{1}{x^{3} - 1}}$$ 
(1/(x - 1) - (x + 1)/(x^2 + x + 1))/(1 + 1/(x^3 - 1))
Descomposición de una fracción [src] 
x^(-2) + 2/x^3
$$\frac{1}{x^{2}} + \frac{2}{x^{3}}$$ 
1    2 
-- + --
 2    3
x    x
Simplificación general [src] 
2 + x
-----
   3 
  x
$$\frac{x + 2}{x^{3}}$$ 
(2 + x)/x^3
Respuesta numérica [src] 
(1/(-1.0 + x) - (1.0 + x)/(1.0 + x + x^2))/(1.0 + 1/(-1.0 + x^3))
(1/(-1.0 + x) - (1.0 + x)/(1.0 + x + x^2))/(1.0 + 1/(-1.0 + x^3))
Parte trigonométrica [src] 
  1        1 + x   
------ - ----------
-1 + x            2
         1 + x + x 
-------------------
           1       
    1 + -------    
              3    
        -1 + x
$$\frac{- \frac{x + 1}{x^{2} + x + 1} + \frac{1}{x - 1}}{1 + \frac{1}{x^{3} - 1}}$$ 
(1/(-1 + x) - (1 + x)/(1 + x + x^2))/(1 + 1/(-1 + x^3))
Potencias [src] 
  1        1 + x   
------ - ----------
-1 + x            2
         1 + x + x 
-------------------
           1       
    1 + -------    
              3    
        -1 + x
$$\frac{- \frac{x + 1}{x^{2} + x + 1} + \frac{1}{x - 1}}{1 + \frac{1}{x^{3} - 1}}$$ 
  1        -1 - x  
------ + ----------
-1 + x            2
         1 + x + x 
-------------------
           1       
    1 + -------    
              3    
        -1 + x
$$\frac{\frac{- x - 1}{x^{2} + x + 1} + \frac{1}{x - 1}}{1 + \frac{1}{x^{3} - 1}}$$ 
(1/(-1 + x) + (-1 - x)/(1 + x + x^2))/(1 + 1/(-1 + x^3))
Combinatoria [src] 
2 + x
-----
   3 
  x
$$\frac{x + 2}{x^{3}}$$ 
(2 + x)/x^3
Unión de expresiones racionales [src] 
/      3\                                   
\-1 + x /*(1 + x*(1 + x) - (1 + x)*(-1 + x))
--------------------------------------------
         3                                  
        x *(1 + x*(1 + x))*(-1 + x)
$$\frac{\left(x^{3} - 1\right) \left(x \left(x + 1\right) - \left(x - 1\right) \left(x + 1\right) + 1\right)}{x^{3} \left(x - 1\right) \left(x \left(x + 1\right) + 1\right)}$$ 
(-1 + x^3)*(1 + x*(1 + x) - (1 + x)*(-1 + x))/(x^3*(1 + x*(1 + x))*(-1 + x))
Denominador común [src] 
2 + x
-----
   3 
  x
$$\frac{x + 2}{x^{3}}$$ 
(2 + x)/x^3
Denominador racional [src] 
/      3\ /         2                    \
\-1 + x /*\1 + x + x  + (-1 + x)*(-1 - x)/
------------------------------------------
          3          /         2\         
         x *(-1 + x)*\1 + x + x /
$$\frac{\left(x^{3} - 1\right) \left(x^{2} + x + \left(- x - 1\right) \left(x - 1\right) + 1\right)}{x^{3} \left(x - 1\right) \left(x^{2} + x + 1\right)}$$ 
(-1 + x^3)*(1 + x + x^2 + (-1 + x)*(-1 - x))/(x^3*(-1 + x)*(1 + x + x^2))
Compilar la expresión [src] 
  1        1 + x   
------ - ----------
-1 + x            2
         1 + x + x 
-------------------
           1       
    1 + -------    
              3    
        -1 + x
$$\frac{- \frac{x + 1}{x^{2} + x + 1} + \frac{1}{x - 1}}{1 + \frac{1}{x^{3} - 1}}$$ 
(1/(-1 + x) - (1 + x)/(1 + x + x^2))/(1 + 1/(-1 + x^3))
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