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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
          sinh(x)           
----------------------------
     ______________         
    /        1          2   
   /  1 - -------- *cosh (x)
  /           2             
\/        cosh (x)
sinh⁡(x)1−1cosh⁡2(x)cosh⁡2(x)\frac{\sinh{\left(x \right)}}{\sqrt{1 - \frac{1}{\cosh^{2}{\left(x \right)}}} \cosh^{2}{\left(x \right)}} 
sinh(x)/((sqrt(1 - 1/cosh(x)^2)*cosh(x)^2))
Simplificación general [src] 
       sinh(x)        
----------------------
   __________         
  /     2         2   
\/  tanh (x) *cosh (x)
sinh⁡(x)tanh⁡2(x)cosh⁡2(x)\frac{\sinh{\left(x \right)}}{\sqrt{\tanh^{2}{\left(x \right)}} \cosh^{2}{\left(x \right)}} 
sinh(x)/(sqrt(tanh(x)^2)*cosh(x)^2)
Respuesta numérica [src] 
(1.0 - 1/cosh(x)^2)^(-0.5)*sinh(x)/cosh(x)^2
(1.0 - 1/cosh(x)^2)^(-0.5)*sinh(x)/cosh(x)^2
Unión de expresiones racionales [src] 
           sinh(x)            
------------------------------
      _______________         
     /          2             
    /  -1 + cosh (x)      2   
   /   ------------- *cosh (x)
  /           2               
\/        cosh (x)
sinh⁡(x)cosh⁡2(x)−1cosh⁡2(x)cosh⁡2(x)\frac{\sinh{\left(x \right)}}{\sqrt{\frac{\cosh^{2}{\left(x \right)} - 1}{\cosh^{2}{\left(x \right)}}} \cosh^{2}{\left(x \right)}} 
sinh(x)/(sqrt((-1 + cosh(x)^2)/cosh(x)^2)*cosh(x)^2)
Combinatoria [src] 
                  sinh(x)                   
--------------------------------------------
    _______________________________         
   /  /       1   \ /        1   \      2   
  /  -|1 + -------|*|-1 + -------| *cosh (x)
\/    \    cosh(x)/ \     cosh(x)/
sinh⁡(x)−(−1+1cosh⁡(x))(1+1cosh⁡(x))cosh⁡2(x)\frac{\sinh{\left(x \right)}}{\sqrt{- \left(-1 + \frac{1}{\cosh{\left(x \right)}}\right) \left(1 + \frac{1}{\cosh{\left(x \right)}}\right)} \cosh^{2}{\left(x \right)}} 
sinh(x)/(sqrt(-(1 + 1/cosh(x))*(-1 + 1/cosh(x)))*cosh(x)^2)
Parte trigonométrica [src] 
       sinh(x)        
----------------------
   __________         
  /     2         2   
\/  tanh (x) *cosh (x)
sinh⁡(x)tanh⁡2(x)cosh⁡2(x)\frac{\sinh{\left(x \right)}}{\sqrt{\tanh^{2}{\left(x \right)}} \cosh^{2}{\left(x \right)}} 
sinh(x)/(sqrt(tanh(x)^2)*cosh(x)^2)
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