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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(-x/(-1+x))*(-1+x/(-1+x))*(2/x+2/(-1+x)+(-1+x/(-1+x))/x)/(4*x)

¿Cómo vas a descomponer esta sqrt(-x/(-1+x))*(-1+x/(-1+x))*(2/x+2/(-1+x)+(-1+x/(-1+x))/x)/(4*x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                           /                    x   \
    ________               |             -1 + ------|
   /  -x     /       x   \ |2     2           -1 + x|
  /  ------ *|-1 + ------|*|- + ------ + -----------|
\/   -1 + x  \     -1 + x/ \x   -1 + x        x     /
-----------------------------------------------------
                         4*x
(−1)xx−1(xx−1−1)((2x−1+2x)+xx−1−1x)4x\frac{\sqrt{\frac{\left(-1\right) x}{x - 1}} \left(\frac{x}{x - 1} - 1\right) \left(\left(\frac{2}{x - 1} + \frac{2}{x}\right) + \frac{\frac{x}{x - 1} - 1}{x}\right)}{4 x} 
((sqrt((-x)/(-1 + x))*(-1 + x/(-1 + x)))*(2/x + 2/(-1 + x) + (-1 + x/(-1 + x))/x))/((4*x))
Simplificación general [src] 
    ________           
   /  -x               
  /  ------ *(-1/4 + x)
\/   -1 + x            
-----------------------
       2         2     
      x *(-1 + x)
−xx−1(x−14)x2(x−1)2\frac{\sqrt{- \frac{x}{x - 1}} \left(x - \frac{1}{4}\right)}{x^{2} \left(x - 1\right)^{2}} 
sqrt(-x/(-1 + x))*(-1/4 + x)/(x^2*(-1 + x)^2)
Respuesta numérica [src] 
0.25*(-x/(-1.0 + x))^0.5*(-1.0 + x/(-1.0 + x))*(2.0/x + 2.0/(-1.0 + x) + (-1.0 + x/(-1.0 + x))/x)/x
0.25*(-x/(-1.0 + x))^0.5*(-1.0 + x/(-1.0 + x))*(2.0/x + 2.0/(-1.0 + x) + (-1.0 + x/(-1.0 + x))/x)/x
Unión de expresiones racionales [src] 
    ________           
   /  -x               
  /  ------ *(-1 + 4*x)
\/   -1 + x            
-----------------------
        2         2    
     4*x *(-1 + x)
−xx−1(4x−1)4x2(x−1)2\frac{\sqrt{- \frac{x}{x - 1}} \left(4 x - 1\right)}{4 x^{2} \left(x - 1\right)^{2}} 
sqrt(-x/(-1 + x))*(-1 + 4*x)/(4*x^2*(-1 + x)^2)
Compilar la expresión [src] 
                           /                    x   \
    ________               |             -1 + ------|
   /  -x     /       x   \ |2     2           -1 + x|
  /  ------ *|-1 + ------|*|- + ------ + -----------|
\/   -1 + x  \     -1 + x/ \x   -1 + x        x     /
-----------------------------------------------------
                         4*x
−xx−1(xx−1−1)(2x−1+xx−1−1x+2x)4x\frac{\sqrt{- \frac{x}{x - 1}} \left(\frac{x}{x - 1} - 1\right) \left(\frac{2}{x - 1} + \frac{\frac{x}{x - 1} - 1}{x} + \frac{2}{x}\right)}{4 x} 
sqrt(-x/(-1 + x))*(-1 + x/(-1 + x))*(2/x + 2/(-1 + x) + (-1 + x/(-1 + x))/x)/(4*x)
Parte trigonométrica [src] 
                           /                    x   \
    ________               |             -1 + ------|
   /  -x     /       x   \ |2     2           -1 + x|
  /  ------ *|-1 + ------|*|- + ------ + -----------|
\/   -1 + x  \     -1 + x/ \x   -1 + x        x     /
-----------------------------------------------------
                         4*x
−xx−1(xx−1−1)(2x−1+xx−1−1x+2x)4x\frac{\sqrt{- \frac{x}{x - 1}} \left(\frac{x}{x - 1} - 1\right) \left(\frac{2}{x - 1} + \frac{\frac{x}{x - 1} - 1}{x} + \frac{2}{x}\right)}{4 x} 
sqrt(-x/(-1 + x))*(-1 + x/(-1 + x))*(2/x + 2/(-1 + x) + (-1 + x/(-1 + x))/x)/(4*x)
Denominador racional [src] 
      ________           ________
     /  -x              /  -x    
-   /  ------  + 4*x*  /  ------ 
  \/   -1 + x        \/   -1 + x 
---------------------------------
             2         2         
          4*x *(-1 + x)
4x−xx−1−−xx−14x2(x−1)2\frac{4 x \sqrt{- \frac{x}{x - 1}} - \sqrt{- \frac{x}{x - 1}}}{4 x^{2} \left(x - 1\right)^{2}} 
(-sqrt(-x/(-1 + x)) + 4*x*sqrt(-x/(-1 + x)))/(4*x^2*(-1 + x)^2)
Abrimos la expresión [src] 
                           /                    x   \
    ________               |             -1 + ------|
   /  -x     /       x   \ |2     2           -1 + x|
  /  ------ *|-1 + ------|*|- + ------ + -----------|
\/   -1 + x  \     -1 + x/ \x   -1 + x        x     /
-----------------------------------------------------
                         4*x
−xx−1(xx−1−1)((2x−1+2x)+xx−1−1x)4x\frac{\sqrt{- \frac{x}{x - 1}} \left(\frac{x}{x - 1} - 1\right) \left(\left(\frac{2}{x - 1} + \frac{2}{x}\right) + \frac{\frac{x}{x - 1} - 1}{x}\right)}{4 x} 
                                  /                    x   \
    ________                      |             -1 + ------|
   /   1       ____ /       x   \ |2     2           -1 + x|
  /  ------ *\/ -x *|-1 + ------|*|- + ------ + -----------|
\/   -1 + x         \     -1 + x/ \x   -1 + x        x     /
------------------------------------------------------------
                            4*x
−x(xx−1−1)((2x−1+2x)+xx−1−1x)1x−14x\frac{\sqrt{- x} \left(\frac{x}{x - 1} - 1\right) \left(\left(\frac{2}{x - 1} + \frac{2}{x}\right) + \frac{\frac{x}{x - 1} - 1}{x}\right) \sqrt{\frac{1}{x - 1}}}{4 x} 
sqrt(1/(-1 + x))*sqrt(-x)*(-1 + x/(-1 + x))*(2/x + 2/(-1 + x) + (-1 + x/(-1 + x))/x)/(4*x)
Combinatoria [src] 
    ________           
   /  -x               
  /  ------ *(-1 + 4*x)
\/   -1 + x            
-----------------------
        2         2    
     4*x *(-1 + x)
−xx−1(4x−1)4x2(x−1)2\frac{\sqrt{- \frac{x}{x - 1}} \left(4 x - 1\right)}{4 x^{2} \left(x - 1\right)^{2}} 
sqrt(-x/(-1 + x))*(-1 + 4*x)/(4*x^2*(-1 + x)^2)
Denominador común [src] 
      ________           ________
     /  -x              /  -x    
-   /  ------  + 4*x*  /  ------ 
  \/   -1 + x        \/   -1 + x 
---------------------------------
            3      2      4      
       - 8*x  + 4*x  + 4*x
4x−xx−1−−xx−14x4−8x3+4x2\frac{4 x \sqrt{- \frac{x}{x - 1}} - \sqrt{- \frac{x}{x - 1}}}{4 x^{4} - 8 x^{3} + 4 x^{2}} 
(-sqrt(-x/(-1 + x)) + 4*x*sqrt(-x/(-1 + x)))/(-8*x^3 + 4*x^2 + 4*x^4)
Potencias [src] 
                           /                    x   \
    ________               |             -1 + ------|
   /  -x     /       x   \ |2     2           -1 + x|
  /  ------ *|-1 + ------|*|- + ------ + -----------|
\/   -1 + x  \     -1 + x/ \x   -1 + x        x     /
-----------------------------------------------------
                         4*x
−xx−1(xx−1−1)(2x−1+xx−1−1x+2x)4x\frac{\sqrt{- \frac{x}{x - 1}} \left(\frac{x}{x - 1} - 1\right) \left(\frac{2}{x - 1} + \frac{\frac{x}{x - 1} - 1}{x} + \frac{2}{x}\right)}{4 x} 
sqrt(-x/(-1 + x))*(-1 + x/(-1 + x))*(2/x + 2/(-1 + x) + (-1 + x/(-1 + x))/x)/(4*x)
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