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Simplificación de expresiones/ Descomposición en fracciones simples/ (5(x-1)^2-2(5x-2)(x-1))/(x-1)^4

¿Cómo vas a descomponer esta (5(x-1)^2-2(5x-2)(x-1))/(x-1)^4 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
         2                      
5*(x - 1)  - 2*(5*x - 2)*(x - 1)
--------------------------------
                   4            
            (x - 1)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) 2 \left(5 x - 2\right)}{\left(x - 1\right)^{4}}$$ 
(5*(x - 1)^2 - 2*(5*x - 2)*(x - 1))/(x - 1)^4
Descomposición de una fracción [src] 
-6/(-1 + x)^3 - 5/(-1 + x)^2
$$- \frac{5}{\left(x - 1\right)^{2}} - \frac{6}{\left(x - 1\right)^{3}}$$ 
      6           5    
- --------- - ---------
          3           2
  (-1 + x)    (-1 + x)
Simplificación general [src] 
-(1 + 5*x) 
-----------
         3 
 (-1 + x)
$$- \frac{5 x + 1}{\left(x - 1\right)^{3}}$$ 
-(1 + 5*x)/(-1 + x)^3
Respuesta numérica [src] 
(5.0*(-1.0 + x)^2 - (-1.0 + x)*(-4.0 + 10.0*x))/(-1.0 + x)^4
(5.0*(-1.0 + x)^2 - (-1.0 + x)*(-4.0 + 10.0*x))/(-1.0 + x)^4
Parte trigonométrica [src] 
          2                       
5*(-1 + x)  - (-1 + x)*(-4 + 10*x)
----------------------------------
                    4             
            (-1 + x)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) \left(10 x - 4\right)}{\left(x - 1\right)^{4}}$$ 
(5*(-1 + x)^2 - (-1 + x)*(-4 + 10*x))/(-1 + x)^4
Compilar la expresión [src] 
          2                       
5*(-1 + x)  - (-1 + x)*(-4 + 10*x)
----------------------------------
                    4             
            (-1 + x)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) \left(10 x - 4\right)}{\left(x - 1\right)^{4}}$$ 
(5*(-1 + x)^2 - (-1 + x)*(-4 + 10*x))/(-1 + x)^4
Unión de expresiones racionales [src] 
 -1 - 5*x
---------
        3
(-1 + x)
$$\frac{- 5 x - 1}{\left(x - 1\right)^{3}}$$ 
(-1 - 5*x)/(-1 + x)^3
Denominador racional [src] 
          2                       
5*(-1 + x)  - (-1 + x)*(-4 + 10*x)
----------------------------------
                    4             
            (-1 + x)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) \left(10 x - 4\right)}{\left(x - 1\right)^{4}}$$ 
(5*(-1 + x)^2 - (-1 + x)*(-4 + 10*x))/(-1 + x)^4
Denominador común [src] 
    -(1 + 5*x)      
--------------------
      3      2      
-1 + x  - 3*x  + 3*x
$$- \frac{5 x + 1}{x^{3} - 3 x^{2} + 3 x - 1}$$ 
-(1 + 5*x)/(-1 + x^3 - 3*x^2 + 3*x)
Combinatoria [src] 
-(1 + 5*x) 
-----------
         3 
 (-1 + x)
$$- \frac{5 x + 1}{\left(x - 1\right)^{3}}$$ 
-(1 + 5*x)/(-1 + x)^3
Potencias [src] 
          2                       
5*(-1 + x)  - (-1 + x)*(-4 + 10*x)
----------------------------------
                    4             
            (-1 + x)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) \left(10 x - 4\right)}{\left(x - 1\right)^{4}}$$ 
(5*(-1 + x)^2 - (-1 + x)*(-4 + 10*x))/(-1 + x)^4
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