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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
       x                   2*x         
      e                   e            
------------- - -----------------------
   __________      __________    ______
  /      2*x      /      2*x    /  2*x 
\/  1 - e       \/  1 - E    *\/  e
ex1−e2x−e2x1−e2xe2x\frac{e^{x}}{\sqrt{1 - e^{2 x}}} - \frac{e^{2 x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} 
exp(x)/sqrt(1 - exp(2*x)) - exp(2*x)/(sqrt(1 - E^(2*x))*sqrt(exp(2*x)))
Simplificación general [src] 
  /   ______     \     
  |  /  2*x     x|  x  
  \\/  e     - e /*e   
-----------------------
   __________    ______
  /      2*x    /  2*x 
\/  1 - e    *\/  e
(−ex+e2x)ex1−e2xe2x\frac{\left(- e^{x} + \sqrt{e^{2 x}}\right) e^{x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} 
(sqrt(exp(2*x)) - exp(x))*exp(x)/(sqrt(1 - exp(2*x))*sqrt(exp(2*x)))
Respuesta numérica [src] 
(1.0 - exp(2*x))^(-0.5)*exp(x) - (1.0 - 2.71828182845905^(2.0*x))^(-0.5)*exp(2*x)^(-0.5)*exp(2*x)
(1.0 - exp(2*x))^(-0.5)*exp(x) - (1.0 - 2.71828182845905^(2.0*x))^(-0.5)*exp(2*x)^(-0.5)*exp(2*x)
Compilar la expresión [src] 
       x                   2*x         
      e                   e            
------------- - -----------------------
   __________      __________    ______
  /      2*x      /      2*x    /  2*x 
\/  1 - e       \/  1 - e    *\/  e
−e2x1−e2xe2x+ex1−e2x- \frac{e^{2 x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} + \frac{e^{x}}{\sqrt{1 - e^{2 x}}} 
exp(x)/sqrt(1 - exp(2*x)) - exp(2*x)/(sqrt(1 - exp(2*x))*sqrt(exp(2*x)))
Denominador común [src] 
 /     ______          \ 
 |    /  2*x   x    2*x| 
-\- \/  e    *e  + e   / 
-------------------------
    __________    ______ 
   /      2*x    /  2*x  
 \/  1 - e    *\/  e
−e2x−exe2x1−e2xe2x- \frac{e^{2 x} - e^{x} \sqrt{e^{2 x}}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} 
-(-sqrt(exp(2*x))*exp(x) + exp(2*x))/(sqrt(1 - exp(2*x))*sqrt(exp(2*x)))
Denominador racional [src] 
/   __________    ______           __________        \      
|  /      2*x    /  2*x   2*x     /      2*x   x  2*x|  -2*x
\\/  1 - e    *\/  e    *e    - \/  1 - e    *e *e   /*e    
------------------------------------------------------------
                               2*x                          
                         -1 + e
(1−e2xe2xe2x−1−e2xexe2x)e−2xe2x−1\frac{\left(\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}} e^{2 x} - \sqrt{1 - e^{2 x}} e^{x} e^{2 x}\right) e^{- 2 x}}{e^{2 x} - 1} 
(sqrt(1 - exp(2*x))*sqrt(exp(2*x))*exp(2*x) - sqrt(1 - exp(2*x))*exp(x)*exp(2*x))*exp(-2*x)/(-1 + exp(2*x))
Potencias [src] 
       x                   2*x         
      e                   e            
------------- - -----------------------
   __________      __________    ______
  /      2*x      /      2*x    /  2*x 
\/  1 - e       \/  1 - e    *\/  e
−e2x1−e2xe2x+ex1−e2x- \frac{e^{2 x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} + \frac{e^{x}}{\sqrt{1 - e^{2 x}}} 
       x                 2*x        
      e                 e           
------------- - --------------------
   __________      _________________
  /      2*x      / /     2*x\  2*x 
\/  1 - e       \/  \1 - e   /*e
ex1−e2x−e2x(1−e2x)e2x\frac{e^{x}}{\sqrt{1 - e^{2 x}}} - \frac{e^{2 x}}{\sqrt{\left(1 - e^{2 x}\right) e^{2 x}}} 
exp(x)/sqrt(1 - exp(2*x)) - exp(2*x)/sqrt((1 - exp(2*x))*exp(2*x))
Unión de expresiones racionales [src] 
  /   ______     \     
  |  /  2*x     x|  x  
  \\/  e     - e /*e   
-----------------------
   __________    ______
  /      2*x    /  2*x 
\/  1 - e    *\/  e
(−ex+e2x)ex1−e2xe2x\frac{\left(- e^{x} + \sqrt{e^{2 x}}\right) e^{x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} 
(sqrt(exp(2*x)) - exp(x))*exp(x)/(sqrt(1 - exp(2*x))*sqrt(exp(2*x)))
Parte trigonométrica [src] 
       x                   2*x         
      e                   e            
------------- - -----------------------
   __________      __________    ______
  /      2*x      /      2*x    /  2*x 
\/  1 - e       \/  1 - e    *\/  e
−e2x1−e2xe2x+ex1−e2x- \frac{e^{2 x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} + \frac{e^{x}}{\sqrt{1 - e^{2 x}}} 
    _______________________                    
- \/ cosh(2*x) + sinh(2*x)  + cosh(x) + sinh(x)
-----------------------------------------------
           ___________________________         
         \/ 1 - cosh(2*x) - sinh(2*x)
−sinh⁡(2x)+cosh⁡(2x)+sinh⁡(x)+cosh⁡(x)−sinh⁡(2x)−cosh⁡(2x)+1\frac{- \sqrt{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}} + \sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sqrt{- \sinh{\left(2 x \right)} - \cosh{\left(2 x \right)} + 1}} 
                                    _______________________  
      cosh(x) + sinh(x)           \/ cosh(2*x) + sinh(2*x)   
----------------------------- - -----------------------------
  ___________________________     ___________________________
\/ 1 - cosh(2*x) - sinh(2*x)    \/ 1 - cosh(2*x) - sinh(2*x)
sinh⁡(x)+cosh⁡(x)−sinh⁡(2x)−cosh⁡(2x)+1−sinh⁡(2x)+cosh⁡(2x)−sinh⁡(2x)−cosh⁡(2x)+1\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sqrt{- \sinh{\left(2 x \right)} - \cosh{\left(2 x \right)} + 1}} - \frac{\sqrt{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}}{\sqrt{- \sinh{\left(2 x \right)} - \cosh{\left(2 x \right)} + 1}} 
                                     _______________________   
      cosh(x) + sinh(x)            \/ cosh(2*x) + sinh(2*x)    
----------------------------- - -------------------------------
  ___________________________      ____________________________
\/ 1 - cosh(2*x) - sinh(2*x)      /                        2*x 
                                \/  1 - (cosh(1) + sinh(1))
sinh⁡(x)+cosh⁡(x)−sinh⁡(2x)−cosh⁡(2x)+1−sinh⁡(2x)+cosh⁡(2x)1−(sinh⁡(1)+cosh⁡(1))2x\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sqrt{- \sinh{\left(2 x \right)} - \cosh{\left(2 x \right)} + 1}} - \frac{\sqrt{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}}{\sqrt{1 - \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{2 x}}} 
(cosh(x) + sinh(x))/sqrt(1 - cosh(2*x) - sinh(2*x)) - sqrt(cosh(2*x) + sinh(2*x))/sqrt(1 - (cosh(1) + sinh(1))^(2*x))
Combinatoria [src] 
      /     ______     \          
      |    /  2*x     x|  x       
     -\- \/  e     + e /*e        
----------------------------------
   _____________________    ______
  /  /     x\ /      x\    /  2*x 
\/  -\1 + e /*\-1 + e / *\/  e
−(ex−e2x)ex−(ex−1)(ex+1)e2x- \frac{\left(e^{x} - \sqrt{e^{2 x}}\right) e^{x}}{\sqrt{- \left(e^{x} - 1\right) \left(e^{x} + 1\right)} \sqrt{e^{2 x}}} 
-(-sqrt(exp(2*x)) + exp(x))*exp(x)/(sqrt(-(1 + exp(x))*(-1 + exp(x)))*sqrt(exp(2*x)))
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