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Simplificación de expresiones/ Descomposición en fracciones simples/ exp(x)/(x+3)^2+(-6-2*x)*exp(x)/(x+3)^4

¿Cómo vas a descomponer esta exp(x)/(x+3)^2+(-6-2*x)*exp(x)/(x+3)^4 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    x                  x
   e       (-6 - 2*x)*e 
-------- + -------------
       2             4  
(x + 3)       (x + 3)
(−2x−6)ex(x+3)4+ex(x+3)2\frac{\left(- 2 x - 6\right) e^{x}}{\left(x + 3\right)^{4}} + \frac{e^{x}}{\left(x + 3\right)^{2}} 
exp(x)/(x + 3)^2 + ((-6 - 2*x)*exp(x))/(x + 3)^4
Simplificación general [src] 
/            2      \  x
\-6 + (3 + x)  - 2*x/*e 
------------------------
               4        
        (3 + x)
(−2x+(x+3)2−6)ex(x+3)4\frac{\left(- 2 x + \left(x + 3\right)^{2} - 6\right) e^{x}}{\left(x + 3\right)^{4}} 
(-6 + (3 + x)^2 - 2*x)*exp(x)/(3 + x)^4
Respuesta numérica [src] 
0.111111111111111*exp(x)/(1 + 0.333333333333333*x)^2 + 0.0123456790123457*(-6.0 - 2.0*x)*exp(x)/(1 + 0.333333333333333*x)^4
0.111111111111111*exp(x)/(1 + 0.333333333333333*x)^2 + 0.0123456790123457*(-6.0 - 2.0*x)*exp(x)/(1 + 0.333333333333333*x)^4
Denominador común [src] 
         x    x      
      x*e  + e       
---------------------
      3      2       
27 + x  + 9*x  + 27*x
xex+exx3+9x2+27x+27\frac{x e^{x} + e^{x}}{x^{3} + 9 x^{2} + 27 x + 27} 
(x*exp(x) + exp(x))/(27 + x^3 + 9*x^2 + 27*x)
Combinatoria [src] 
         x
(1 + x)*e 
----------
        3 
 (3 + x)
(x+1)ex(x+3)3\frac{\left(x + 1\right) e^{x}}{\left(x + 3\right)^{3}} 
(1 + x)*exp(x)/(3 + x)^3
Denominador racional [src] 
       4  x          2             x
(3 + x) *e  + (3 + x) *(-6 - 2*x)*e 
------------------------------------
                     6              
              (3 + x)
(−2x−6)(x+3)2ex+(x+3)4ex(x+3)6\frac{\left(- 2 x - 6\right) \left(x + 3\right)^{2} e^{x} + \left(x + 3\right)^{4} e^{x}}{\left(x + 3\right)^{6}} 
((3 + x)^4*exp(x) + (3 + x)^2*(-6 - 2*x)*exp(x))/(3 + x)^6
Unión de expresiones racionales [src] 
/            2      \  x
\-6 + (3 + x)  - 2*x/*e 
------------------------
               4        
        (3 + x)
(−2x+(x+3)2−6)ex(x+3)4\frac{\left(- 2 x + \left(x + 3\right)^{2} - 6\right) e^{x}}{\left(x + 3\right)^{4}} 
(-6 + (3 + x)^2 - 2*x)*exp(x)/(3 + x)^4
Parte trigonométrica [src] 
cosh(x) + sinh(x)   (-6 - 2*x)*(cosh(x) + sinh(x))
----------------- + ------------------------------
            2                         4           
     (3 + x)                   (3 + x)
(−2x−6)(sinh⁡(x)+cosh⁡(x))(x+3)4+sinh⁡(x)+cosh⁡(x)(x+3)2\frac{\left(- 2 x - 6\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(x + 3\right)^{4}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(x + 3\right)^{2}} 
x*cosh(x) + x*sinh(x) + cosh(x) + sinh(x)
-----------------------------------------
                        3                
                 (3 + x)
xsinh⁡(x)+xcosh⁡(x)+sinh⁡(x)+cosh⁡(x)(x+3)3\frac{x \sinh{\left(x \right)} + x \cosh{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(x + 3\right)^{3}} 
(x*cosh(x) + x*sinh(x) + cosh(x) + sinh(x))/(3 + x)^3
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