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

Expresión a simplificar:

Solución

Ha introducido [src]
    _______                                 
   /   x            /    1           x     \
  /  ----- *(b - x)*|--------- + ----------|
\/   b - x          |2*(b - x)            2|
                    \            2*(b - x) /
--------------------------------------------
                 /      x  \                
               x*|1 + -----|                
                 \    b - x/                
$$\frac{\sqrt{\frac{x}{b - x}} \left(b - x\right) \left(\frac{x}{2 \left(b - x\right)^{2}} + \frac{1}{2 \left(b - x\right)}\right)}{x \left(\frac{x}{b - x} + 1\right)}$$
((sqrt(x/(b - x))*(b - x))*(1/(2*(b - x)) + x/((2*(b - x)^2))))/((x*(1 + x/(b - x))))
Simplificación general [src]
    _______
   /   x   
  /  ----- 
\/   b - x 
-----------
    2*x    
$$\frac{\sqrt{\frac{x}{b - x}}}{2 x}$$
sqrt(x/(b - x))/(2*x)
Respuesta numérica [src]
(x/(b - x))^0.5*(b - x)*(1/(2.0*b - 2.0*x) + 0.5*x/(b - x)^2)/(x*(1.0 + x/(b - x)))
(x/(b - x))^0.5*(b - x)*(1/(2.0*b - 2.0*x) + 0.5*x/(b - x)^2)/(x*(1.0 + x/(b - x)))
Parte trigonométrica [src]
    _______                                  
   /   x            /    1            x     \
  /  ----- *(b - x)*|---------- + ----------|
\/   b - x          |-2*x + 2*b            2|
                    \             2*(b - x) /
---------------------------------------------
                  /      x  \                
                x*|1 + -----|                
                  \    b - x/                
$$\frac{\sqrt{\frac{x}{b - x}} \left(b - x\right) \left(\frac{x}{2 \left(b - x\right)^{2}} + \frac{1}{2 b - 2 x}\right)}{x \left(\frac{x}{b - x} + 1\right)}$$
sqrt(x/(b - x))*(b - x)*(1/(-2*x + 2*b) + x/(2*(b - x)^2))/(x*(1 + x/(b - x)))
Unión de expresiones racionales [src]
    _______
   /   x   
  /  ----- 
\/   b - x 
-----------
    2*x    
$$\frac{\sqrt{\frac{x}{b - x}}}{2 x}$$
sqrt(x/(b - x))/(2*x)
Potencias [src]
    _______                                  
   /   x            /    1            x     \
  /  ----- *(b - x)*|---------- + ----------|
\/   b - x          |-2*x + 2*b            2|
                    \             2*(b - x) /
---------------------------------------------
                  /      x  \                
                x*|1 + -----|                
                  \    b - x/                
$$\frac{\sqrt{\frac{x}{b - x}} \left(b - x\right) \left(\frac{x}{2 \left(b - x\right)^{2}} + \frac{1}{2 b - 2 x}\right)}{x \left(\frac{x}{b - x} + 1\right)}$$
sqrt(x/(b - x))*(b - x)*(1/(-2*x + 2*b) + x/(2*(b - x)^2))/(x*(1 + x/(b - x)))
Abrimos la expresión [src]
    _______                                 
   /   1            /    1           x     \
  /  ----- *(b - x)*|--------- + ----------|
\/   b - x          |2*(b - x)            2|
                    \            2*(b - x) /
--------------------------------------------
               ___ /      x  \              
             \/ x *|1 + -----|              
                   \    b - x/              
$$\frac{\left(b - x\right) \left(\frac{x}{2 \left(b - x\right)^{2}} + \frac{1}{2 \left(b - x\right)}\right) \sqrt{\frac{1}{b - x}}}{\sqrt{x} \left(\frac{x}{b - x} + 1\right)}$$
sqrt(1/(b - x))*(b - x)*(1/(2*(b - x)) + x/(2*(b - x)^2))/(sqrt(x)*(1 + x/(b - x)))
Compilar la expresión [src]
    _______                                  
   /   x            /    1            x     \
  /  ----- *(b - x)*|---------- + ----------|
\/   b - x          |-2*x + 2*b            2|
                    \             2*(b - x) /
---------------------------------------------
                  /      x  \                
                x*|1 + -----|                
                  \    b - x/                
$$\frac{\sqrt{\frac{x}{b - x}} \left(b - x\right) \left(\frac{x}{2 \left(b - x\right)^{2}} + \frac{1}{2 b - 2 x}\right)}{x \left(\frac{x}{b - x} + 1\right)}$$
sqrt(x/(b - x))*(b - x)*(1/(-2*x + 2*b) + x/(2*(b - x)^2))/(x*(1 + x/(b - x)))
Denominador común [src]
    _______
   /   x   
  /  ----- 
\/   b - x 
-----------
    2*x    
$$\frac{\sqrt{\frac{x}{b - x}}}{2 x}$$
sqrt(x/(b - x))/(2*x)
Denominador racional [src]
    _______                              
   /   x    /         2                 \
  /  ----- *\2*(b - x)  + x*(-2*x + 2*b)/
\/   b - x                               
-----------------------------------------
            2*b*x*(-2*x + 2*b)           
$$\frac{\sqrt{\frac{x}{b - x}} \left(x \left(2 b - 2 x\right) + 2 \left(b - x\right)^{2}\right)}{2 b x \left(2 b - 2 x\right)}$$
sqrt(x/(b - x))*(2*(b - x)^2 + x*(-2*x + 2*b))/(2*b*x*(-2*x + 2*b))
Combinatoria [src]
    _______
   /   x   
  /  ----- 
\/   b - x 
-----------
    2*x    
$$\frac{\sqrt{\frac{x}{b - x}}}{2 x}$$
sqrt(x/(b - x))/(2*x)