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

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

Expresión a simplificar:

Solución

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