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

Expresión a simplificar:

Solución

Ha introducido [src]
   ____________ /       2               \
3 /          2  |(x - 1)    x*(-2 + 2*x)|
\/  x*(x - 1)  *|-------- + ------------|
                \   3            3      /
-----------------------------------------
                         2               
                x*(x - 1)                
$$\frac{\sqrt[3]{x \left(x - 1\right)^{2}} \left(\frac{x \left(2 x - 2\right)}{3} + \frac{\left(x - 1\right)^{2}}{3}\right)}{x \left(x - 1\right)^{2}}$$
((x*(x - 1)^2)^(1/3)*((x - 1)^2/3 + (x*(-2 + 2*x))/3))/((x*(x - 1)^2))
Simplificación general [src]
   _____________           
3 /           2            
\/  x*(-1 + x)  *(-1/3 + x)
---------------------------
         x*(-1 + x)        
$$\frac{\sqrt[3]{x \left(x - 1\right)^{2}} \left(x - \frac{1}{3}\right)}{x \left(x - 1\right)}$$
(x*(-1 + x)^2)^(1/3)*(-1/3 + x)/(x*(-1 + x))
Respuesta numérica [src]
(x*(-1.0 + x)^2)^0.333333333333333*(0.333333333333333*(-1.0 + x)^2 + 0.333333333333333*x*(-2.0 + 2.0*x))/(x*(-1.0 + x)^2)
(x*(-1.0 + x)^2)^0.333333333333333*(0.333333333333333*(-1.0 + x)^2 + 0.333333333333333*x*(-2.0 + 2.0*x))/(x*(-1.0 + x)^2)
Denominador racional [src]
   _____________                           
3 /           2  /        2               \
\/  x*(-1 + x)  *\(-1 + x)  + x*(-2 + 2*x)/
-------------------------------------------
                           2               
               3*x*(-1 + x)                
$$\frac{\sqrt[3]{x \left(x - 1\right)^{2}} \left(x \left(2 x - 2\right) + \left(x - 1\right)^{2}\right)}{3 x \left(x - 1\right)^{2}}$$
(x*(-1 + x)^2)^(1/3)*((-1 + x)^2 + x*(-2 + 2*x))/(3*x*(-1 + x)^2)
Abrimos la expresión [src]
   __________ /       2               \
3 /        2  |(x - 1)    x*(-2 + 2*x)|
\/  (x - 1)  *|-------- + ------------|
              \   3            3      /
---------------------------------------
              2/3        2             
             x   *(x - 1)              
$$\frac{\left(\frac{x \left(2 x - 2\right)}{3} + \frac{\left(x - 1\right)^{2}}{3}\right) \sqrt[3]{\left(x - 1\right)^{2}}}{x^{\frac{2}{3}} \left(x - 1\right)^{2}}$$
((x - 1)^2)^(1/3)*((x - 1)^2/3 + (x*(-2 + 2*x))/3)/(x^(2/3)*(x - 1)^2)
Denominador común [src]
     _______________          _______________
  3 /      3      2        3 /      3      2 
- \/  x + x  - 2*x   + 3*x*\/  x + x  - 2*x  
---------------------------------------------
                           2                 
                 -3*x + 3*x                  
$$\frac{3 x \sqrt[3]{x^{3} - 2 x^{2} + x} - \sqrt[3]{x^{3} - 2 x^{2} + x}}{3 x^{2} - 3 x}$$
(-(x + x^3 - 2*x^2)^(1/3) + 3*x*(x + x^3 - 2*x^2)^(1/3))/(-3*x + 3*x^2)
Combinatoria [src]
   _____________           
3 /           2            
\/  x*(-1 + x)  *(-1 + 3*x)
---------------------------
        3*x*(-1 + x)       
$$\frac{\sqrt[3]{x \left(x - 1\right)^{2}} \left(3 x - 1\right)}{3 x \left(x - 1\right)}$$
(x*(-1 + x)^2)^(1/3)*(-1 + 3*x)/(3*x*(-1 + x))
Unión de expresiones racionales [src]
   _____________                     
3 /           2             /  1   x\
\/  x*(-1 + x)  *(-1 + 3*x)*|- - + -|
                            \  3   3/
-------------------------------------
                       2             
             x*(-1 + x)              
$$\frac{\sqrt[3]{x \left(x - 1\right)^{2}} \left(\frac{x}{3} - \frac{1}{3}\right) \left(3 x - 1\right)}{x \left(x - 1\right)^{2}}$$
(x*(-1 + x)^2)^(1/3)*(-1 + 3*x)*(-1/3 + x/3)/(x*(-1 + x)^2)