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¿Cómo vas a descomponer esta exp(x)/(x^3+5)-3*x^2*exp(x)/(x^3+5)^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
   x         2  x 
  e       3*x *e  
------ - ---------
 3               2
x  + 5   / 3    \ 
         \x  + 5/ 
$$- \frac{3 x^{2} e^{x}}{\left(x^{3} + 5\right)^{2}} + \frac{e^{x}}{x^{3} + 5}$$
exp(x)/(x^3 + 5) - (3*x^2)*exp(x)/(x^3 + 5)^2
Simplificación general [src]
/     3      2\  x
\5 + x  - 3*x /*e 
------------------
       6       3  
 25 + x  + 10*x   
$$\frac{\left(x^{3} - 3 x^{2} + 5\right) e^{x}}{x^{6} + 10 x^{3} + 25}$$
(5 + x^3 - 3*x^2)*exp(x)/(25 + x^6 + 10*x^3)
Respuesta numérica [src]
exp(x)/(5.0 + x^3) - 0.12*x^2*exp(x)/(1 + 0.2*x^3)^2
exp(x)/(5.0 + x^3) - 0.12*x^2*exp(x)/(1 + 0.2*x^3)^2
Unión de expresiones racionales [src]
/     3      2\  x
\5 + x  - 3*x /*e 
------------------
            2     
    /     3\      
    \5 + x /      
$$\frac{\left(x^{3} - 3 x^{2} + 5\right) e^{x}}{\left(x^{3} + 5\right)^{2}}$$
(5 + x^3 - 3*x^2)*exp(x)/(5 + x^3)^2
Denominador racional [src]
        2                      
/     3\   x      2 /     3\  x
\5 + x / *e  - 3*x *\5 + x /*e 
-------------------------------
                   3           
           /     3\            
           \5 + x /            
$$\frac{- 3 x^{2} \left(x^{3} + 5\right) e^{x} + \left(x^{3} + 5\right)^{2} e^{x}}{\left(x^{3} + 5\right)^{3}}$$
((5 + x^3)^2*exp(x) - 3*x^2*(5 + x^3)*exp(x))/(5 + x^3)^3
Combinatoria [src]
/     3      2\  x
\5 + x  - 3*x /*e 
------------------
            2     
    /     3\      
    \5 + x /      
$$\frac{\left(x^{3} - 3 x^{2} + 5\right) e^{x}}{\left(x^{3} + 5\right)^{2}}$$
(5 + x^3 - 3*x^2)*exp(x)/(5 + x^3)^2
Denominador común [src]
   x    3  x      2  x
5*e  + x *e  - 3*x *e 
----------------------
         6       3    
   25 + x  + 10*x     
$$\frac{x^{3} e^{x} - 3 x^{2} e^{x} + 5 e^{x}}{x^{6} + 10 x^{3} + 25}$$
(5*exp(x) + x^3*exp(x) - 3*x^2*exp(x))/(25 + x^6 + 10*x^3)
Parte trigonométrica [src]
                       2                    
cosh(x) + sinh(x)   3*x *(cosh(x) + sinh(x))
----------------- - ------------------------
           3                       2        
      5 + x                /     3\         
                           \5 + x /         
$$- \frac{3 x^{2} \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(x^{3} + 5\right)^{2}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{x^{3} + 5}$$
(cosh(x) + sinh(x))/(5 + x^3) - 3*x^2*(cosh(x) + sinh(x))/(5 + x^3)^2