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

Expresión a simplificar:

Solución

Ha introducido [src]
   /  x  \          
cot|-----|*x        
   |  ___|       ___
   \\/ y /      / x 
------------*  /  - 
      3/2    \/   3 
   2*y              
--------------------
         _______    
        / x         
   2*  /  - + 1     
     \/   3         
$$\frac{\sqrt{\frac{x}{3}} \frac{x \cot{\left(\frac{x}{\sqrt{y}} \right)}}{2 y^{\frac{3}{2}}}}{2 \sqrt{\frac{x}{3} + 1}}$$
(((cot(x/sqrt(y))*x)/((2*y^(3/2))))*sqrt(x/3))/((2*sqrt(x/3 + 1)))
Simplificación general [src]
 3/2    /  x  \ 
x   *cot|-----| 
        |  ___| 
        \\/ y / 
----------------
   3/2   _______
4*y   *\/ 3 + x 
$$\frac{x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{4 y^{\frac{3}{2}} \sqrt{x + 3}}$$
x^(3/2)*cot(x/sqrt(y))/(4*y^(3/2)*sqrt(3 + x))
Denominador racional [src]
        ____    /    ___\
 3/2   /  3     |x*\/ y |
x   *\/  y  *cot|-------|
                \   y   /
-------------------------
         3   _______     
      4*y *\/ 3 + x      
$$\frac{x^{\frac{3}{2}} \sqrt{y^{3}} \cot{\left(\frac{x \sqrt{y}}{y} \right)}}{4 y^{3} \sqrt{x + 3}}$$
x^(3/2)*sqrt(y^3)*cot(x*sqrt(y)/y)/(4*y^3*sqrt(3 + x))
Denominador común [src]
 3/2    /  x  \ 
x   *cot|-----| 
        |  ___| 
        \\/ y / 
----------------
   3/2   _______
4*y   *\/ 3 + x 
$$\frac{x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{4 y^{\frac{3}{2}} \sqrt{x + 3}}$$
x^(3/2)*cot(x/sqrt(y))/(4*y^(3/2)*sqrt(3 + x))
Potencias [src]
  ___  3/2    /  x  \
\/ 3 *x   *cot|-----|
              |  ___|
              \\/ y /
---------------------
             _______ 
     3/2    /     x  
 12*y   *  /  1 + -  
         \/       3  
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
sqrt(3)*x^(3/2)*cot(x/sqrt(y))/(12*y^(3/2)*sqrt(1 + x/3))
Unión de expresiones racionales [src]
 3/2    /  x  \ 
x   *cot|-----| 
        |  ___| 
        \\/ y / 
----------------
   3/2   _______
4*y   *\/ 3 + x 
$$\frac{x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{4 y^{\frac{3}{2}} \sqrt{x + 3}}$$
x^(3/2)*cot(x/sqrt(y))/(4*y^(3/2)*sqrt(3 + x))
Combinatoria [src]
 3/2    /  x  \ 
x   *cot|-----| 
        |  ___| 
        \\/ y / 
----------------
   3/2   _______
4*y   *\/ 3 + x 
$$\frac{x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{4 y^{\frac{3}{2}} \sqrt{x + 3}}$$
x^(3/2)*cot(x/sqrt(y))/(4*y^(3/2)*sqrt(3 + x))
Compilar la expresión [src]
  ___  3/2    /  x  \
\/ 3 *x   *cot|-----|
              |  ___|
              \\/ y /
---------------------
             _______ 
     3/2    /     x  
 12*y   *  /  1 + -  
         \/       3  
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
sqrt(3)*x^(3/2)*cot(x/sqrt(y))/(12*y^(3/2)*sqrt(1 + x/3))
Abrimos la expresión [src]
  ___  3/2    /  x  \
\/ 3 *x   *cot|-----|
              |  ___|
              \\/ y /
---------------------
             _______ 
     3/2    /     x  
 12*y   *  /  1 + -  
         \/       3  
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
  ___  3/2    /  x  \
\/ 3 *x   *cot|-----|
              |  ___|
              \\/ y /
---------------------
             _______ 
     3/2    / x      
 12*y   *  /  - + 1  
         \/   3      
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
sqrt(3)*x^(3/2)*cot(x/sqrt(y))/(12*y^(3/2)*sqrt(x/3 + 1))
Parte trigonométrica [src]
         ___  3/2    /  x  \       
       \/ 3 *x   *csc|-----|       
                     |  ___|       
                     \\/ y /       
-----------------------------------
            _______                
    3/2    /     x     /pi     x  \
12*y   *  /  1 + - *csc|-- - -----|
        \/       3     |2      ___|
                       \     \/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \csc{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \csc{\left(- \frac{x}{\sqrt{y}} + \frac{\pi}{2} \right)}}$$
   ___  3/2    /  pi     x  \ 
 \/ 3 *x   *sec|- -- + -----| 
               |  2      ___| 
               \       \/ y / 
------------------------------
            _______           
    3/2    /     x     /  x  \
12*y   *  /  1 + - *sec|-----|
        \/       3     |  ___|
                       \\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \sec{\left(\frac{x}{\sqrt{y}} - \frac{\pi}{2} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \sec{\left(\frac{x}{\sqrt{y}} \right)}}$$
            ___  3/2          
          \/ 3 *x             
------------------------------
            _______           
    3/2    /     x     /  x  \
12*y   *  /  1 + - *tan|-----|
        \/       3     |  ___|
                       \\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \tan{\left(\frac{x}{\sqrt{y}} \right)}}$$
      ___  3/2    /  x  \     
    \/ 3 *x   *csc|-----|     
                  |  ___|     
                  \\/ y /     
------------------------------
            _______           
    3/2    /     x     /  x  \
12*y   *  /  1 + - *sec|-----|
        \/       3     |  ___|
                       \\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \csc{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \sec{\left(\frac{x}{\sqrt{y}} \right)}}$$
      ___  3/2    /  x  \     
    \/ 3 *x   *cos|-----|     
                  |  ___|     
                  \\/ y /     
------------------------------
            _______           
    3/2    /     x     /  x  \
12*y   *  /  1 + - *sin|-----|
        \/       3     |  ___|
                       \\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cos{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \sin{\left(\frac{x}{\sqrt{y}} \right)}}$$
          ___  3/2    /  x  \        
        \/ 3 *x   *cos|-----|        
                      |  ___|        
                      \\/ y /        
-------------------------------------
            _______                  
    3/2    /     x     /  pi     x  \
12*y   *  /  1 + - *cos|- -- + -----|
        \/       3     |  2      ___|
                       \       \/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cos{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \cos{\left(\frac{x}{\sqrt{y}} - \frac{\pi}{2} \right)}}$$
  ___  3/2    /  x  \
\/ 3 *x   *cot|-----|
              |  ___|
              \\/ y /
---------------------
             _______ 
     3/2    /     x  
 12*y   *  /  1 + -  
         \/       3  
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
  ___  3/2    /  x  \
\/ 3 *x   *cot|-----|
              |  ___|
              \\/ y /
---------------------
             _______ 
     3/2    / x      
 12*y   *  /  - + 1  
         \/   3      
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
       ___  3/2    / 2*x \     
     \/ 3 *x   *sin|-----|     
                   |  ___|     
                   \\/ y /     
-------------------------------
            _______            
    3/2    /     x     2/  x  \
24*y   *  /  1 + - *sin |-----|
        \/       3      |  ___|
                        \\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \sin{\left(\frac{2 x}{\sqrt{y}} \right)}}{24 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \sin^{2}{\left(\frac{x}{\sqrt{y}} \right)}}$$
sqrt(3)*x^(3/2)*sin(2*x/sqrt(y))/(24*y^(3/2)*sqrt(1 + x/3)*sin(x/sqrt(y))^2)
Respuesta numérica [src]
0.144337567297406*x^1.5*y^(-1.5)*(1.0 + 0.333333333333333*x)^(-0.5)*cot(x/sqrt(y))
0.144337567297406*x^1.5*y^(-1.5)*(1.0 + 0.333333333333333*x)^(-0.5)*cot(x/sqrt(y))