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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    x           x   
   e         2*e    
------- - ----------
2*x - 1            2
          (2*x - 1)
−2ex(2x−1)2+ex2x−1- \frac{2 e^{x}}{\left(2 x - 1\right)^{2}} + \frac{e^{x}}{2 x - 1} 
exp(x)/(2*x - 1) - 2*exp(x)/(2*x - 1)^2
Simplificación general [src] 
            x 
(-3 + 2*x)*e  
--------------
             2
1 - 4*x + 4*x
(2x−3)ex4x2−4x+1\frac{\left(2 x - 3\right) e^{x}}{4 x^{2} - 4 x + 1} 
(-3 + 2*x)*exp(x)/(1 - 4*x + 4*x^2)
Respuesta numérica [src] 
exp(x)/(-1.0 + 2.0*x) - 0.5*exp(x)/(-0.5 + x)^2
exp(x)/(-1.0 + 2.0*x) - 0.5*exp(x)/(-0.5 + x)^2
Compilar la expresión [src] 
    x             x   
   e           2*e    
-------- - -----------
-1 + 2*x             2
           (-1 + 2*x)
ex2x−1−2ex(2x−1)2\frac{e^{x}}{2 x - 1} - \frac{2 e^{x}}{\left(2 x - 1\right)^{2}} 
exp(x)/(-1 + 2*x) - 2*exp(x)/(-1 + 2*x)^2
Denominador común [src] 
     x        x
- 3*e  + 2*x*e 
---------------
              2
 1 - 4*x + 4*x
2xex−3ex4x2−4x+1\frac{2 x e^{x} - 3 e^{x}}{4 x^{2} - 4 x + 1} 
(-3*exp(x) + 2*x*exp(x))/(1 - 4*x + 4*x^2)
Combinatoria [src] 
            x
(-3 + 2*x)*e 
-------------
           2 
 (-1 + 2*x)
(2x−3)ex(2x−1)2\frac{\left(2 x - 3\right) e^{x}}{\left(2 x - 1\right)^{2}} 
(-3 + 2*x)*exp(x)/(-1 + 2*x)^2
Potencias [src] 
    x             x   
   e           2*e    
-------- - -----------
-1 + 2*x             2
           (-1 + 2*x)
ex2x−1−2ex(2x−1)2\frac{e^{x}}{2 x - 1} - \frac{2 e^{x}}{\left(2 x - 1\right)^{2}} 
exp(x)/(-1 + 2*x) - 2*exp(x)/(-1 + 2*x)^2
Denominador racional [src] 
          2  x                 x
(-1 + 2*x) *e  - 2*(-1 + 2*x)*e 
--------------------------------
                    3           
          (-1 + 2*x)
(2x−1)2ex−2(2x−1)ex(2x−1)3\frac{\left(2 x - 1\right)^{2} e^{x} - 2 \left(2 x - 1\right) e^{x}}{\left(2 x - 1\right)^{3}} 
((-1 + 2*x)^2*exp(x) - 2*(-1 + 2*x)*exp(x))/(-1 + 2*x)^3
Unión de expresiones racionales [src] 
            x
(-3 + 2*x)*e 
-------------
           2 
 (-1 + 2*x)
(2x−3)ex(2x−1)2\frac{\left(2 x - 3\right) e^{x}}{\left(2 x - 1\right)^{2}} 
(-3 + 2*x)*exp(x)/(-1 + 2*x)^2
Parte trigonométrica [src] 
cosh(x) + sinh(x)   2*cosh(x) + 2*sinh(x)
----------------- - ---------------------
     -1 + 2*x                      2     
                         (-1 + 2*x)
sinh⁡(x)+cosh⁡(x)2x−1−2sinh⁡(x)+2cosh⁡(x)(2x−1)2\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{2 x - 1} - \frac{2 \sinh{\left(x \right)} + 2 \cosh{\left(x \right)}}{\left(2 x - 1\right)^{2}} 
cosh(x) + sinh(x)   2*(cosh(x) + sinh(x))
----------------- - ---------------------
     -1 + 2*x                      2     
                         (-1 + 2*x)
sinh⁡(x)+cosh⁡(x)2x−1−2(sinh⁡(x)+cosh⁡(x))(2x−1)2\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{2 x - 1} - \frac{2 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(2 x - 1\right)^{2}} 
    x             x   
   e           2*e    
-------- - -----------
-1 + 2*x             2
           (-1 + 2*x)
ex2x−1−2ex(2x−1)2\frac{e^{x}}{2 x - 1} - \frac{2 e^{x}}{\left(2 x - 1\right)^{2}} 
exp(x)/(-1 + 2*x) - 2*exp(x)/(-1 + 2*x)^2
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