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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt((x/(x+1))^2)*(x+1)*(2/(x+1)-2*x/(x+1)^2)/(2*x)

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

Expresión a simplificar:

Solución

Ha introducido [src] 
     __________                           
    /        2                            
   /  /  x  \           /  2       2*x   \
  /   |-----|  *(x + 1)*|----- - --------|
\/    \x + 1/           |x + 1          2|
                        \        (x + 1) /
------------------------------------------
                   2*x
(x+1)(xx+1)2(−2x(x+1)2+2x+1)2x\frac{\left(x + 1\right) \sqrt{\left(\frac{x}{x + 1}\right)^{2}} \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right)}{2 x} 
((sqrt((x/(x + 1))^2)*(x + 1))*(2/(x + 1) - 2*x/(x + 1)^2))/((2*x))
Simplificación general [src] 
      __________
     /     2    
    /     x     
   /   -------- 
  /           2 
\/     (1 + x)  
----------------
   x*(1 + x)
x2(x+1)2x(x+1)\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}}}{x \left(x + 1\right)} 
sqrt(x^2/(1 + x)^2)/(x*(1 + x))
Respuesta numérica [src] 
0.5*(x^2/(1.0 + x)^2)^0.5*(1.0 + x)*(2.0/(1.0 + x) - 2.0*x/(1.0 + x)^2)/x
0.5*(x^2/(1.0 + x)^2)^0.5*(1.0 + x)*(2.0/(1.0 + x) - 2.0*x/(1.0 + x)^2)/x
Denominador racional [src] 
            __________              __________           __________         
           /     2                 /     2              /     2             
          /     x           2     /     x              /     x             2
- 2*x*   /   --------  - 2*x *   /   --------  + 2*   /   -------- *(1 + x) 
        /           2           /           2        /           2          
      \/     (x + 1)          \/     (x + 1)       \/     (x + 1)           
----------------------------------------------------------------------------
                                           2                                
                                2*x*(1 + x)
−2x2x2(x+1)2−2xx2(x+1)2+2x2(x+1)2(x+1)22x(x+1)2\frac{- 2 x^{2} \sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} - 2 x \sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} + 2 \sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} \left(x + 1\right)^{2}}{2 x \left(x + 1\right)^{2}} 
(-2*x*sqrt(x^2/(x + 1)^2) - 2*x^2*sqrt(x^2/(x + 1)^2) + 2*sqrt(x^2/(x + 1)^2)*(1 + x)^2)/(2*x*(1 + x)^2)
Unión de expresiones racionales [src] 
      __________
     /     2    
    /     x     
   /   -------- 
  /           2 
\/     (1 + x)  
----------------
   x*(1 + x)
x2(x+1)2x(x+1)\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}}}{x \left(x + 1\right)} 
sqrt(x^2/(1 + x)^2)/(x*(1 + x))
Parte trigonométrica [src] 
      __________                           
     /     2                               
    /     x              /  2       2*x   \
   /   -------- *(1 + x)*|----- - --------|
  /           2          |1 + x          2|
\/     (1 + x)           \        (1 + x) /
-------------------------------------------
                    2*x
x2(x+1)2(x+1)(−2x(x+1)2+2x+1)2x\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} \left(x + 1\right) \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right)}{2 x} 
sqrt(x^2/(1 + x)^2)*(1 + x)*(2/(1 + x) - 2*x/(1 + x)^2)/(2*x)
Potencias [src] 
      __________                           
     /     2                               
    /     x              /  2       2*x   \
   /   -------- *(1 + x)*|----- - --------|
  /           2          |1 + x          2|
\/     (1 + x)           \        (1 + x) /
-------------------------------------------
                    2*x
x2(x+1)2(x+1)(−2x(x+1)2+2x+1)2x\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} \left(x + 1\right) \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right)}{2 x} 
sqrt(x^2/(1 + x)^2)*(1 + x)*(2/(1 + x) - 2*x/(1 + x)^2)/(2*x)
Abrimos la expresión [src] 
      __________                           
     /     2                               
    /     x              /  2       2*x   \
   /   -------- *(x + 1)*|----- - --------|
  /           2          |x + 1          2|
\/     (x + 1)           \        (x + 1) /
-------------------------------------------
                    2*x
x2(x+1)2(x+1)(−2x(x+1)2+2x+1)2x\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} \left(x + 1\right) \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right)}{2 x} 
   ____      __________                           
  /  2      /    1              /  2       2*x   \
\/  x  *   /  -------- *(x + 1)*|----- - --------|
          /          2          |x + 1          2|
        \/    (x + 1)           \        (x + 1) /
--------------------------------------------------
                       2*x
(x+1)(−2x(x+1)2+2x+1)x21(x+1)22x\frac{\left(x + 1\right) \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right) \sqrt{x^{2}} \sqrt{\frac{1}{\left(x + 1\right)^{2}}}}{2 x} 
sqrt(x^2)*sqrt((x + 1)^(-2))*(x + 1)*(2/(x + 1) - 2*x/(x + 1)^2)/(2*x)
Combinatoria [src] 
      ______________
     /       2      
    /       x       
   /   ------------ 
  /         2       
\/     1 + x  + 2*x 
--------------------
     x*(1 + x)
x2x2+2x+1x(x+1)\frac{\sqrt{\frac{x^{2}}{x^{2} + 2 x + 1}}}{x \left(x + 1\right)} 
sqrt(x^2/(1 + x^2 + 2*x))/(x*(1 + x))
Compilar la expresión [src] 
      __________                           
     /     2                               
    /     x              /  2       2*x   \
   /   -------- *(1 + x)*|----- - --------|
  /           2          |1 + x          2|
\/     (1 + x)           \        (1 + x) /
-------------------------------------------
                    2*x
x2(x+1)2(x+1)(−2x(x+1)2+2x+1)2x\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} \left(x + 1\right) \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right)}{2 x} 
sqrt(x^2/(1 + x)^2)*(1 + x)*(2/(1 + x) - 2*x/(1 + x)^2)/(2*x)
Denominador común [src] 
      ______________
     /       2      
    /       x       
   /   ------------ 
  /         2       
\/     1 + x  + 2*x 
--------------------
            2       
       x + x
x2x2+2x+1x2+x\frac{\sqrt{\frac{x^{2}}{x^{2} + 2 x + 1}}}{x^{2} + x} 
sqrt(x^2/(1 + x^2 + 2*x))/(x + x^2)
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