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¿Cómo vas a descomponer esta sqrt(4*x^3/(x+3))*(x+3)*(-2*x^3/(x+3)^2+6*x^2/(x+3))/(4*x^3) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
     _______                           
    /     3          /     3         2\
   /   4*x           | -2*x       6*x |
  /   ----- *(x + 3)*|-------- + -----|
\/    x + 3          |       2   x + 3|
                     \(x + 3)         /
---------------------------------------
                     3                 
                  4*x                  
4x3x+3(x+3)(6x2x+3+(1)2x3(x+3)2)4x3\frac{\sqrt{\frac{4 x^{3}}{x + 3}} \left(x + 3\right) \left(\frac{6 x^{2}}{x + 3} + \frac{\left(-1\right) 2 x^{3}}{\left(x + 3\right)^{2}}\right)}{4 x^{3}}
((sqrt((4*x^3)/(x + 3))*(x + 3))*((-2*x^3)/(x + 3)^2 + (6*x^2)/(x + 3)))/((4*x^3))
Simplificación general [src]
     _______          
    /    3            
   /    x             
  /   ----- *(9 + 2*x)
\/    3 + x           
----------------------
      x*(3 + x)       
x3x+3(2x+9)x(x+3)\frac{\sqrt{\frac{x^{3}}{x + 3}} \left(2 x + 9\right)}{x \left(x + 3\right)}
sqrt(x^3/(3 + x))*(9 + 2*x)/(x*(3 + x))
Abrimos la expresión [src]
     _______                           
    /    3           /     3         2\
   /    x            | -2*x       6*x |
  /   ----- *(x + 3)*|-------- + -----|
\/    x + 3          |       2   x + 3|
                     \(x + 3)         /
---------------------------------------
                     3                 
                  2*x                  
x3x+3(x+3)(6x2x+3+(1)2x3(x+3)2)2x3\frac{\sqrt{\frac{x^{3}}{x + 3}} \left(x + 3\right) \left(\frac{6 x^{2}}{x + 3} + \frac{\left(-1\right) 2 x^{3}}{\left(x + 3\right)^{2}}\right)}{2 x^{3}}
   ____     _______         /     3         2\
  /  3     /   1            | -2*x       6*x |
\/  x  *  /  ----- *(x + 3)*|-------- + -----|
        \/   x + 3          |       2   x + 3|
                            \(x + 3)         /
----------------------------------------------
                        3                     
                     2*x                      
(x+3)(6x2x+3+(1)2x3(x+3)2)x31x+32x3\frac{\left(x + 3\right) \left(\frac{6 x^{2}}{x + 3} + \frac{\left(-1\right) 2 x^{3}}{\left(x + 3\right)^{2}}\right) \sqrt{x^{3}} \sqrt{\frac{1}{x + 3}}}{2 x^{3}}
sqrt(x^3)*sqrt(1/(x + 3))*(x + 3)*((-2*x^3)/(x + 3)^2 + (6*x^2)/(x + 3))/(2*x^3)
Unión de expresiones racionales [src]
     _______          
    /    3            
   /    x             
  /   ----- *(9 + 2*x)
\/    3 + x           
----------------------
      x*(3 + x)       
x3x+3(2x+9)x(x+3)\frac{\sqrt{\frac{x^{3}}{x + 3}} \left(2 x + 9\right)}{x \left(x + 3\right)}
sqrt(x^3/(3 + x))*(9 + 2*x)/(x*(3 + x))
Denominador común [src]
       _______            _______
      /    3             /    3  
     /    x             /    x   
9*  /   -----  + 2*x*  /   ----- 
  \/    3 + x        \/    3 + x 
---------------------------------
              2                  
             x  + 3*x            
2xx3x+3+9x3x+3x2+3x\frac{2 x \sqrt{\frac{x^{3}}{x + 3}} + 9 \sqrt{\frac{x^{3}}{x + 3}}}{x^{2} + 3 x}
(9*sqrt(x^3/(3 + x)) + 2*x*sqrt(x^3/(3 + x)))/(x^2 + 3*x)
Respuesta numérica [src]
0.5*(x^3/(3.0 + x))^0.5*(3.0 + x)*(6.0*x^2/(3.0 + x) - 0.222222222222222*x^3/(1 + 0.333333333333333*x)^2)/x^3
0.5*(x^3/(3.0 + x))^0.5*(3.0 + x)*(6.0*x^2/(3.0 + x) - 0.222222222222222*x^3/(1 + 0.333333333333333*x)^2)/x^3
Potencias [src]
     _______                               
    /    3             /       3         2\
   /    x              |    2*x       6*x |
  /   ----- *(6 + 2*x)*|- -------- + -----|
\/    3 + x            |         2   3 + x|
                       \  (3 + x)         /
-------------------------------------------
                       3                   
                    4*x                    
x3x+3(2x+6)(2x3(x+3)2+6x2x+3)4x3\frac{\sqrt{\frac{x^{3}}{x + 3}} \left(2 x + 6\right) \left(- \frac{2 x^{3}}{\left(x + 3\right)^{2}} + \frac{6 x^{2}}{x + 3}\right)}{4 x^{3}}
     _______                             
    /    3           /       3         2\
   /    x            |    2*x       6*x |
  /   ----- *(3 + x)*|- -------- + -----|
\/    3 + x          |         2   3 + x|
                     \  (3 + x)         /
-----------------------------------------
                      3                  
                   2*x                   
x3x+3(x+3)(2x3(x+3)2+6x2x+3)2x3\frac{\sqrt{\frac{x^{3}}{x + 3}} \left(x + 3\right) \left(- \frac{2 x^{3}}{\left(x + 3\right)^{2}} + \frac{6 x^{2}}{x + 3}\right)}{2 x^{3}}
sqrt(x^3/(3 + x))*(3 + x)*(-2*x^3/(3 + x)^2 + 6*x^2/(3 + x))/(2*x^3)
Combinatoria [src]
     _______          
    /    3            
   /    x             
  /   ----- *(9 + 2*x)
\/    3 + x           
----------------------
      x*(3 + x)       
x3x+3(2x+9)x(x+3)\frac{\sqrt{\frac{x^{3}}{x + 3}} \left(2 x + 9\right)}{x \left(x + 3\right)}
sqrt(x^3/(3 + x))*(9 + 2*x)/(x*(3 + x))
Denominador racional [src]
     _______                                 
    /    3                                   
   /    x    /     3              2        2\
  /   ----- *\- 2*x *(3 + x) + 6*x *(3 + x) /
\/    x + 3                                  
---------------------------------------------
                   3        2                
                2*x *(3 + x)                 
x3x+3(2x3(x+3)+6x2(x+3)2)2x3(x+3)2\frac{\sqrt{\frac{x^{3}}{x + 3}} \left(- 2 x^{3} \left(x + 3\right) + 6 x^{2} \left(x + 3\right)^{2}\right)}{2 x^{3} \left(x + 3\right)^{2}}
sqrt(x^3/(x + 3))*(-2*x^3*(3 + x) + 6*x^2*(3 + x)^2)/(2*x^3*(3 + x)^2)
Compilar la expresión [src]
     _______                             
    /    3           /       3         2\
   /    x            |    2*x       6*x |
  /   ----- *(3 + x)*|- -------- + -----|
\/    3 + x          |         2   3 + x|
                     \  (3 + x)         /
-----------------------------------------
                      3                  
                   2*x                   
x3x+3(x+3)(2x3(x+3)2+6x2x+3)2x3\frac{\sqrt{\frac{x^{3}}{x + 3}} \left(x + 3\right) \left(- \frac{2 x^{3}}{\left(x + 3\right)^{2}} + \frac{6 x^{2}}{x + 3}\right)}{2 x^{3}}
sqrt(x^3/(3 + x))*(3 + x)*(-2*x^3/(3 + x)^2 + 6*x^2/(3 + x))/(2*x^3)
Parte trigonométrica [src]
     _______                             
    /    3           /       3         2\
   /    x            |    2*x       6*x |
  /   ----- *(3 + x)*|- -------- + -----|
\/    3 + x          |         2   3 + x|
                     \  (3 + x)         /
-----------------------------------------
                      3                  
                   2*x                   
x3x+3(x+3)(2x3(x+3)2+6x2x+3)2x3\frac{\sqrt{\frac{x^{3}}{x + 3}} \left(x + 3\right) \left(- \frac{2 x^{3}}{\left(x + 3\right)^{2}} + \frac{6 x^{2}}{x + 3}\right)}{2 x^{3}}
sqrt(x^3/(3 + x))*(3 + x)*(-2*x^3/(3 + x)^2 + 6*x^2/(3 + x))/(2*x^3)