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

Expresión a simplificar:

Solución

Ha introducido [src]
     ___________                                   
    /  3      2          /          2    3      2 \
   /  x  - 2*x           |-4*x + 3*x    x  - 2*x  |
  /   --------- *(x - 3)*|----------- - ----------|
\/      x - 3            | 2*(x - 3)             2|
                         \              2*(x - 3) /
---------------------------------------------------
                      3      2                     
                     x  - 2*x                      
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(- \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}} + \frac{3 x^{2} - 4 x}{2 \left(x - 3\right)}\right)}{x^{3} - 2 x^{2}}$$
((sqrt((x^3 - 2*x^2)/(x - 3))*(x - 3))*((-4*x + 3*x^2)/((2*(x - 3))) - (x^3 - 2*x^2)/(2*(x - 3)^2)))/(x^3 - 2*x^2)
Simplificación general [src]
     _____________                
    /  2                          
   /  x *(-2 + x)  /     2   11*x\
  /   ----------- *|6 + x  - ----|
\/       -3 + x    \          2  /
----------------------------------
           /     2      \         
         x*\6 + x  - 5*x/         
$$\frac{\sqrt{\frac{x^{2} \left(x - 2\right)}{x - 3}} \left(x^{2} - \frac{11 x}{2} + 6\right)}{x \left(x^{2} - 5 x + 6\right)}$$
sqrt(x^2*(-2 + x)/(-3 + x))*(6 + x^2 - 11*x/2)/(x*(6 + x^2 - 5*x))
Respuesta numérica [src]
((x^3 - 2.0*x^2)/(-3.0 + x))^0.5*(-3.0 + x)*((3.0*x^2 - 4.0*x)/(-6.0 + 2.0*x) - 0.0555555555555556*(x^3 - 2.0*x^2)/(-1 + 0.333333333333333*x)^2)/(x^3 - 2.0*x^2)
((x^3 - 2.0*x^2)/(-3.0 + x))^0.5*(-3.0 + x)*((3.0*x^2 - 4.0*x)/(-6.0 + 2.0*x) - 0.0555555555555556*(x^3 - 2.0*x^2)/(-1 + 0.333333333333333*x)^2)/(x^3 - 2.0*x^2)
Abrimos la expresión [src]
    _______         /          2    3      2 \
   /   1            |-4*x + 3*x    x  - 2*x  |
  /  ----- *(x - 3)*|----------- - ----------|
\/   x - 3          | 2*(x - 3)             2|
                    \              2*(x - 3) /
----------------------------------------------
                   ___________                
                  /  3      2                 
                \/  x  - 2*x                  
$$\frac{\left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 \left(x - 3\right)} - \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}}\right) \sqrt{\frac{1}{x - 3}}}{\sqrt{x^{3} - 2 x^{2}}}$$
     ___________                                   
    /  3      2          /          2    3      2 \
   /  x  - 2*x           |-4*x + 3*x    x  - 2*x  |
  /   --------- *(x - 3)*|----------- - ----------|
\/      x - 3            | 2*(x - 3)             2|
                         \              2*(x - 3) /
---------------------------------------------------
                      3      2                     
                     x  - 2*x                      
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 \left(x - 3\right)} - \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}}\right)}{x^{3} - 2 x^{2}}$$
sqrt((x^3 - 2*x^2)/(x - 3))*(x - 3)*((-4*x + 3*x^2)/(2*(x - 3)) - (x^3 - 2*x^2)/(2*(x - 3)^2))/(x^3 - 2*x^2)
Denominador racional [src]
     ___________                                                       
    /  3      2                                                        
   /  x  - 2*x   /           /   3      2\             2 /          2\\
  /   --------- *\(-6 + 2*x)*\- x  + 2*x / + 2*(-3 + x) *\-4*x + 3*x //
\/      x - 3                                                          
-----------------------------------------------------------------------
                                         / 3      2\                   
                   2*(-6 + 2*x)*(-3 + x)*\x  - 2*x /                   
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(2 \left(x - 3\right)^{2} \left(3 x^{2} - 4 x\right) + \left(2 x - 6\right) \left(- x^{3} + 2 x^{2}\right)\right)}{2 \left(x - 3\right) \left(2 x - 6\right) \left(x^{3} - 2 x^{2}\right)}$$
sqrt((x^3 - 2*x^2)/(x - 3))*((-6 + 2*x)*(-x^3 + 2*x^2) + 2*(-3 + x)^2*(-4*x + 3*x^2))/(2*(-6 + 2*x)*(-3 + x)*(x^3 - 2*x^2))
Combinatoria [src]
     _____________                    
    /  2                              
   /  x *(-2 + x)                     
  /   ----------- *(-4 + x)*(-3 + 2*x)
\/       -3 + x                       
--------------------------------------
        2*x*(-3 + x)*(-2 + x)         
$$\frac{\sqrt{\frac{x^{2} \left(x - 2\right)}{x - 3}} \left(x - 4\right) \left(2 x - 3\right)}{2 x \left(x - 3\right) \left(x - 2\right)}$$
sqrt(x^2*(-2 + x)/(-3 + x))*(-4 + x)*(-3 + 2*x)/(2*x*(-3 + x)*(-2 + x))
Parte trigonométrica [src]
     ___________                                     
    /  3      2           /          2     3      2 \
   /  x  - 2*x            |-4*x + 3*x     x  - 2*x  |
  /   --------- *(-3 + x)*|----------- - -----------|
\/      -3 + x            |  -6 + 2*x              2|
                          \              2*(-3 + x) /
-----------------------------------------------------
                       3      2                      
                      x  - 2*x                       
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 x - 6} - \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}}\right)}{x^{3} - 2 x^{2}}$$
sqrt((x^3 - 2*x^2)/(-3 + x))*(-3 + x)*((-4*x + 3*x^2)/(-6 + 2*x) - (x^3 - 2*x^2)/(2*(-3 + x)^2))/(x^3 - 2*x^2)
Compilar la expresión [src]
     ___________                                     
    /  3      2           /          2     3      2 \
   /  x  - 2*x            |-4*x + 3*x     x  - 2*x  |
  /   --------- *(-3 + x)*|----------- - -----------|
\/      -3 + x            |  -6 + 2*x              2|
                          \              2*(-3 + x) /
-----------------------------------------------------
                       3      2                      
                      x  - 2*x                       
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 x - 6} - \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}}\right)}{x^{3} - 2 x^{2}}$$
sqrt((x^3 - 2*x^2)/(-3 + x))*(-3 + x)*((-4*x + 3*x^2)/(-6 + 2*x) - (x^3 - 2*x^2)/(2*(-3 + x)^2))/(x^3 - 2*x^2)
Unión de expresiones racionales [src]
     _____________                                   
    /  2                                             
   /  x *(-2 + x)                                    
  /   ----------- *((-4 + 3*x)*(-3 + x) - x*(-2 + x))
\/       -3 + x                                      
-----------------------------------------------------
                2*x*(-3 + x)*(-2 + x)                
$$\frac{\sqrt{\frac{x^{2} \left(x - 2\right)}{x - 3}} \left(- x \left(x - 2\right) + \left(x - 3\right) \left(3 x - 4\right)\right)}{2 x \left(x - 3\right) \left(x - 2\right)}$$
sqrt(x^2*(-2 + x)/(-3 + x))*((-4 + 3*x)*(-3 + x) - x*(-2 + x))/(2*x*(-3 + x)*(-2 + x))
Potencias [src]
     ___________                                     
    /  3      2           /          2     3      2 \
   /  x  - 2*x            |-4*x + 3*x     x  - 2*x  |
  /   --------- *(-3 + x)*|----------- - -----------|
\/      -3 + x            |  -6 + 2*x              2|
                          \              2*(-3 + x) /
-----------------------------------------------------
                       3      2                      
                      x  - 2*x                       
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 x - 6} - \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}}\right)}{x^{3} - 2 x^{2}}$$
                          /                     3 \
     ___________          |                2   x  |
    /  3      2           |          2    x  - -- |
   /  x  - 2*x            |-4*x + 3*x          2  |
  /   --------- *(-3 + x)*|----------- + ---------|
\/      -3 + x            |  -6 + 2*x            2|
                          \              (-3 + x) /
---------------------------------------------------
                      3      2                     
                     x  - 2*x                      
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 x - 6} + \frac{- \frac{x^{3}}{2} + x^{2}}{\left(x - 3\right)^{2}}\right)}{x^{3} - 2 x^{2}}$$
sqrt((x^3 - 2*x^2)/(-3 + x))*(-3 + x)*((-4*x + 3*x^2)/(-6 + 2*x) + (x^2 - x^3/2)/(-3 + x)^2)/(x^3 - 2*x^2)
Denominador común [src]
        _________________             _________________             _________________
       /    3         2              /    3         2              /    3         2  
      /    x       2*x              /    x       2*x         2    /    x       2*x   
12*  /   ------ - ------  - 11*x*  /   ------ - ------  + 2*x *  /   ------ - ------ 
   \/    -3 + x   -3 + x         \/    -3 + x   -3 + x         \/    -3 + x   -3 + x 
-------------------------------------------------------------------------------------
                                      2      3                                       
                                - 10*x  + 2*x  + 12*x                                
$$\frac{2 x^{2} \sqrt{\frac{x^{3}}{x - 3} - \frac{2 x^{2}}{x - 3}} - 11 x \sqrt{\frac{x^{3}}{x - 3} - \frac{2 x^{2}}{x - 3}} + 12 \sqrt{\frac{x^{3}}{x - 3} - \frac{2 x^{2}}{x - 3}}}{2 x^{3} - 10 x^{2} + 12 x}$$
(12*sqrt(x^3/(-3 + x) - 2*x^2/(-3 + x)) - 11*x*sqrt(x^3/(-3 + x) - 2*x^2/(-3 + x)) + 2*x^2*sqrt(x^3/(-3 + x) - 2*x^2/(-3 + x)))/(-10*x^2 + 2*x^3 + 12*x)