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¿Cómo vas a descomponer esta 2*(-4+3*(2*x-1)/(x-1))/(x-1)^3 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
  /     3*(2*x - 1)\
2*|-4 + -----------|
  \        x - 1   /
--------------------
             3      
      (x - 1)       
$$\frac{2 \left(-4 + \frac{3 \left(2 x - 1\right)}{x - 1}\right)}{\left(x - 1\right)^{3}}$$
(2*(-4 + (3*(2*x - 1))/(x - 1)))/(x - 1)^3
Descomposición de una fracción [src]
4/(-1 + x)^3 + 6/(-1 + x)^4
$$\frac{4}{\left(x - 1\right)^{3}} + \frac{6}{\left(x - 1\right)^{4}}$$
    4           6    
--------- + ---------
        3           4
(-1 + x)    (-1 + x) 
Simplificación general [src]
2*(1 + 2*x)
-----------
         4 
 (-1 + x)  
$$\frac{2 \left(2 x + 1\right)}{\left(x - 1\right)^{4}}$$
2*(1 + 2*x)/(-1 + x)^4
Respuesta numérica [src]
(-8.0 + 2.0*(-3.0 + 6.0*x)/(-1.0 + x))/(-1.0 + x)^3
(-8.0 + 2.0*(-3.0 + 6.0*x)/(-1.0 + x))/(-1.0 + x)^3
Compilar la expresión [src]
     2*(-3 + 6*x)
-8 + ------------
        -1 + x   
-----------------
            3    
    (-1 + x)     
$$\frac{-8 + \frac{2 \left(6 x - 3\right)}{x - 1}}{\left(x - 1\right)^{3}}$$
(-8 + 2*(-3 + 6*x)/(-1 + x))/(-1 + x)^3
Denominador racional [src]
 2 + 4*x 
---------
        4
(-1 + x) 
$$\frac{4 x + 2}{\left(x - 1\right)^{4}}$$
(2 + 4*x)/(-1 + x)^4
Parte trigonométrica [src]
     2*(-3 + 6*x)
-8 + ------------
        -1 + x   
-----------------
            3    
    (-1 + x)     
$$\frac{-8 + \frac{2 \left(6 x - 3\right)}{x - 1}}{\left(x - 1\right)^{3}}$$
(-8 + 2*(-3 + 6*x)/(-1 + x))/(-1 + x)^3
Denominador común [src]
         2 + 4*x          
--------------------------
     4            3      2
1 + x  - 4*x - 4*x  + 6*x 
$$\frac{4 x + 2}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1}$$
(2 + 4*x)/(1 + x^4 - 4*x - 4*x^3 + 6*x^2)
Combinatoria [src]
2*(1 + 2*x)
-----------
         4 
 (-1 + x)  
$$\frac{2 \left(2 x + 1\right)}{\left(x - 1\right)^{4}}$$
2*(1 + 2*x)/(-1 + x)^4
Unión de expresiones racionales [src]
2*(1 + 2*x)
-----------
         4 
 (-1 + x)  
$$\frac{2 \left(2 x + 1\right)}{\left(x - 1\right)^{4}}$$
2*(1 + 2*x)/(-1 + x)^4
Potencias [src]
     2*(-3 + 6*x)
-8 + ------------
        -1 + x   
-----------------
            3    
    (-1 + x)     
$$\frac{-8 + \frac{2 \left(6 x - 3\right)}{x - 1}}{\left(x - 1\right)^{3}}$$
     -6 + 12*x
-8 + ---------
       -1 + x 
--------------
          3   
  (-1 + x)    
$$\frac{-8 + \frac{12 x - 6}{x - 1}}{\left(x - 1\right)^{3}}$$
(-8 + (-6 + 12*x)/(-1 + x))/(-1 + x)^3