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

Expresión a simplificar:

Solución

Ha introducido [src]
     _______                                 
    /    3           /     3             2  \
   /    x            |   -x           3*x   |
  /   ----- *(x - 1)*|---------- + ---------|
\/    x - 1          |         2   2*(x - 1)|
                     \2*(x - 1)             /
---------------------------------------------
                       3                     
                      x                      
x3x1(x1)(3x22(x1)+(1)x32(x1)2)x3\frac{\sqrt{\frac{x^{3}}{x - 1}} \left(x - 1\right) \left(\frac{3 x^{2}}{2 \left(x - 1\right)} + \frac{\left(-1\right) x^{3}}{2 \left(x - 1\right)^{2}}\right)}{x^{3}}
((sqrt(x^3/(x - 1))*(x - 1))*((-x^3)/((2*(x - 1)^2)) + (3*x^2)/((2*(x - 1)))))/x^3
Simplificación general [src]
     ________           
    /    3              
   /    x               
  /   ------ *(-3/2 + x)
\/    -1 + x            
------------------------
       x*(-1 + x)       
x3x1(x32)x(x1)\frac{\sqrt{\frac{x^{3}}{x - 1}} \left(x - \frac{3}{2}\right)}{x \left(x - 1\right)}
sqrt(x^3/(-1 + x))*(-3/2 + x)/(x*(-1 + x))
Abrimos la expresión [src]
     _______                                   
    /    3           /       3             2  \
   /    x            |      x           3*x   |
  /   ----- *(x - 1)*|- ---------- + ---------|
\/    x - 1          |           2   2*(x - 1)|
                     \  2*(x - 1)             /
-----------------------------------------------
                        3                      
                       x                       
x3x1(x1)(x32(x1)2+3x22(x1))x3\frac{\sqrt{\frac{x^{3}}{x - 1}} \left(x - 1\right) \left(- \frac{x^{3}}{2 \left(x - 1\right)^{2}} + \frac{3 x^{2}}{2 \left(x - 1\right)}\right)}{x^{3}}
    _______         /       3             2  \
   /   1            |      x           3*x   |
  /  ----- *(x - 1)*|- ---------- + ---------|
\/   x - 1          |           2   2*(x - 1)|
                    \  2*(x - 1)             /
----------------------------------------------
                      ____                    
                     /  3                     
                   \/  x                      
(x1)(x32(x1)2+3x22(x1))1x1x3\frac{\left(x - 1\right) \left(- \frac{x^{3}}{2 \left(x - 1\right)^{2}} + \frac{3 x^{2}}{2 \left(x - 1\right)}\right) \sqrt{\frac{1}{x - 1}}}{\sqrt{x^{3}}}
sqrt(1/(x - 1))*(x - 1)*(-x^3/(2*(x - 1)^2) + 3*x^2/(2*(x - 1)))/sqrt(x^3)
Parte trigonométrica [src]
     ________                                  
    /    3             /     2           3    \
   /    x              |  3*x           x     |
  /   ------ *(-1 + x)*|-------- - -----------|
\/    -1 + x           |-2 + 2*x             2|
                       \           2*(-1 + x) /
-----------------------------------------------
                        3                      
                       x                       
x3x1(x1)(x32(x1)2+3x22x2)x3\frac{\sqrt{\frac{x^{3}}{x - 1}} \left(x - 1\right) \left(- \frac{x^{3}}{2 \left(x - 1\right)^{2}} + \frac{3 x^{2}}{2 x - 2}\right)}{x^{3}}
sqrt(x^3/(-1 + x))*(-1 + x)*(3*x^2/(-2 + 2*x) - x^3/(2*(-1 + x)^2))/x^3
Respuesta numérica [src]
(x^3/(-1.0 + x))^0.5*(-1.0 + x)*(3.0*x^2/(-2.0 + 2.0*x) - 0.5*x^3/(-1.0 + x)^2)/x^3
(x^3/(-1.0 + x))^0.5*(-1.0 + x)*(3.0*x^2/(-2.0 + 2.0*x) - 0.5*x^3/(-1.0 + x)^2)/x^3
Combinatoria [src]
     ________           
    /    3              
   /    x               
  /   ------ *(-3 + 2*x)
\/    -1 + x            
------------------------
      2*x*(-1 + x)      
x3x1(2x3)2x(x1)\frac{\sqrt{\frac{x^{3}}{x - 1}} \left(2 x - 3\right)}{2 x \left(x - 1\right)}
sqrt(x^3/(-1 + x))*(-3 + 2*x)/(2*x*(-1 + x))
Potencias [src]
     ________                                  
    /    3             /     2           3    \
   /    x              |  3*x           x     |
  /   ------ *(-1 + x)*|-------- - -----------|
\/    -1 + x           |-2 + 2*x             2|
                       \           2*(-1 + x) /
-----------------------------------------------
                        3                      
                       x                       
x3x1(x1)(x32(x1)2+3x22x2)x3\frac{\sqrt{\frac{x^{3}}{x - 1}} \left(x - 1\right) \left(- \frac{x^{3}}{2 \left(x - 1\right)^{2}} + \frac{3 x^{2}}{2 x - 2}\right)}{x^{3}}
sqrt(x^3/(-1 + x))*(-1 + x)*(3*x^2/(-2 + 2*x) - x^3/(2*(-1 + x)^2))/x^3
Denominador común [src]
         ________            ________
        /    3              /    3   
       /    x              /    x    
- 3*  /   ------  + 2*x*  /   ------ 
    \/    -1 + x        \/    -1 + x 
-------------------------------------
                       2             
             -2*x + 2*x              
2xx3x13x3x12x22x\frac{2 x \sqrt{\frac{x^{3}}{x - 1}} - 3 \sqrt{\frac{x^{3}}{x - 1}}}{2 x^{2} - 2 x}
(-3*sqrt(x^3/(-1 + x)) + 2*x*sqrt(x^3/(-1 + x)))/(-2*x + 2*x^2)
Unión de expresiones racionales [src]
     ________           
    /    3              
   /    x               
  /   ------ *(-3 + 2*x)
\/    -1 + x            
------------------------
      2*x*(-1 + x)      
x3x1(2x3)2x(x1)\frac{\sqrt{\frac{x^{3}}{x - 1}} \left(2 x - 3\right)}{2 x \left(x - 1\right)}
sqrt(x^3/(-1 + x))*(-3 + 2*x)/(2*x*(-1 + x))
Denominador racional [src]
     _______                                   
    /    3                                     
   /    x    /   3                 2         2\
  /   ----- *\- x *(-2 + 2*x) + 6*x *(-1 + x) /
\/    x - 1                                    
-----------------------------------------------
               3                               
            2*x *(-1 + x)*(-2 + 2*x)           
x3x1(x3(2x2)+6x2(x1)2)2x3(x1)(2x2)\frac{\sqrt{\frac{x^{3}}{x - 1}} \left(- x^{3} \left(2 x - 2\right) + 6 x^{2} \left(x - 1\right)^{2}\right)}{2 x^{3} \left(x - 1\right) \left(2 x - 2\right)}
sqrt(x^3/(x - 1))*(-x^3*(-2 + 2*x) + 6*x^2*(-1 + x)^2)/(2*x^3*(-1 + x)*(-2 + 2*x))
Compilar la expresión [src]
     ________                                  
    /    3             /     2           3    \
   /    x              |  3*x           x     |
  /   ------ *(-1 + x)*|-------- - -----------|
\/    -1 + x           |-2 + 2*x             2|
                       \           2*(-1 + x) /
-----------------------------------------------
                        3                      
                       x                       
x3x1(x1)(x32(x1)2+3x22x2)x3\frac{\sqrt{\frac{x^{3}}{x - 1}} \left(x - 1\right) \left(- \frac{x^{3}}{2 \left(x - 1\right)^{2}} + \frac{3 x^{2}}{2 x - 2}\right)}{x^{3}}
sqrt(x^3/(-1 + x))*(-1 + x)*(3*x^2/(-2 + 2*x) - x^3/(2*(-1 + x)^2))/x^3