Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ exp(1/(x-3))/((x-3)^2*(x-3)^2)-(6-2*x)*exp(1/(x-3))/(x-3)^4

¿Cómo vas a descomponer esta exp(1/(x-3))/((x-3)^2*(x-3)^2)-(6-2*x)*exp(1/(x-3))/(x-3)^4 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
         1                       1  
       -----                   -----
       x - 3                   x - 3
      e             (6 - 2*x)*e     
----------------- - ----------------
       2        2              4    
(x - 3) *(x - 3)        (x - 3)
−(6−2x)e1x−3(x−3)4+e1x−3(x−3)2(x−3)2- \frac{\left(6 - 2 x\right) e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} + \frac{e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{2} \left(x - 3\right)^{2}} 
exp(1/(x - 3))/(((x - 3)^2*(x - 3)^2)) - (6 - 2*x)*exp(1/(x - 3))/(x - 3)^4
Simplificación general [src] 
              1   
            ------
            -3 + x
(-5 + 2*x)*e      
------------------
            4     
    (-3 + x)
(2x−5)e1x−3(x−3)4\frac{\left(2 x - 5\right) e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} 
(-5 + 2*x)*exp(1/(-3 + x))/(-3 + x)^4
Respuesta numérica [src] 
0.0123456790123457*exp(1/(x - 3))/(-1 + 0.333333333333333*x)^4 - 0.0123456790123457*(6.0 - 2.0*x)*exp(1/(x - 3))/(-1 + 0.333333333333333*x)^4
0.0123456790123457*exp(1/(x - 3))/(-1 + 0.333333333333333*x)^4 - 0.0123456790123457*(6.0 - 2.0*x)*exp(1/(x - 3))/(-1 + 0.333333333333333*x)^4
Abrimos la expresión [src] 
    1                   1  
  -----               -----
  x - 3               x - 3
 e         (6 - 2*x)*e     
-------- - ----------------
       4              4    
(x - 3)        (x - 3)
−(6−2x)e1x−3(x−3)4+e1x−3(x−3)4- \frac{\left(6 - 2 x\right) e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} + \frac{e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} 
exp(1/(x - 3))/(x - 3)^4 - (6 - 2*x)*exp(1/(x - 3))/(x - 3)^4
Compilar la expresión [src] 
     1                   1  
   -----               -----
   x - 3               x - 3
  e         (6 - 2*x)*e     
--------- - ----------------
        4              4    
(-3 + x)       (-3 + x)
−(6−2x)e1x−3(x−3)4+e1x−3(x−3)4- \frac{\left(6 - 2 x\right) e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} + \frac{e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} 
exp(1/(x - 3))/(-3 + x)^4 - (6 - 2*x)*exp(1/(x - 3))/(-3 + x)^4
Potencias [src] 
    1                    1   
  ------               ------
  -3 + x               -3 + x
 e          (6 - 2*x)*e      
--------- - -----------------
        4               4    
(-3 + x)        (-3 + x)
−(6−2x)e1x−3(x−3)4+e1x−3(x−3)4- \frac{\left(6 - 2 x\right) e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} + \frac{e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} 
    1                     1   
  ------                ------
  -3 + x                -3 + x
 e          (-6 + 2*x)*e      
--------- + ------------------
        4               4     
(-3 + x)        (-3 + x)
(2x−6)e1x−3(x−3)4+e1x−3(x−3)4\frac{\left(2 x - 6\right) e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} + \frac{e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} 
exp(1/(-3 + x))/(-3 + x)^4 + (-6 + 2*x)*exp(1/(-3 + x))/(-3 + x)^4
Combinatoria [src] 
              1   
            ------
            -3 + x
(-5 + 2*x)*e      
------------------
            4     
    (-3 + x)
(2x−5)e1x−3(x−3)4\frac{\left(2 x - 5\right) e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} 
(-5 + 2*x)*exp(1/(-3 + x))/(-3 + x)^4
Unión de expresiones racionales [src] 
              1   
            ------
            -3 + x
(-5 + 2*x)*e      
------------------
            4     
    (-3 + x)
(2x−5)e1x−3(x−3)4\frac{\left(2 x - 5\right) e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} 
(-5 + 2*x)*exp(1/(-3 + x))/(-3 + x)^4
Denominador racional [src] 
               1        1  
             -----    -----
             x - 3    x - 3
- (6 - 2*x)*e      + e     
---------------------------
                 4         
         (-3 + x)
−(6−2x)e1x−3+e1x−3(x−3)4\frac{- \left(6 - 2 x\right) e^{\frac{1}{x - 3}} + e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} 
(-(6 - 2*x)*exp(1/(x - 3)) + exp(1/(x - 3)))/(-3 + x)^4
Denominador común [src] 
          1             1      
        ------        ------   
        -3 + x        -3 + x   
   - 5*e       + 2*x*e         
-------------------------------
      4               3       2
81 + x  - 108*x - 12*x  + 54*x
2xe1x−3−5e1x−3x4−12x3+54x2−108x+81\frac{2 x e^{\frac{1}{x - 3}} - 5 e^{\frac{1}{x - 3}}}{x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81} 
(-5*exp(1/(-3 + x)) + 2*x*exp(1/(-3 + x)))/(81 + x^4 - 108*x - 12*x^3 + 54*x^2)
Parte trigonométrica [src] 
        /  1   \         /  1   \           /  1   \           /  1   \
- 5*cosh|------| - 5*sinh|------| + 2*x*cosh|------| + 2*x*sinh|------|
        \-3 + x/         \-3 + x/           \-3 + x/           \-3 + x/
-----------------------------------------------------------------------
                                       4                               
                               (-3 + x)
2xsinh⁡(1x−3)+2xcosh⁡(1x−3)−5sinh⁡(1x−3)−5cosh⁡(1x−3)(x−3)4\frac{2 x \sinh{\left(\frac{1}{x - 3} \right)} + 2 x \cosh{\left(\frac{1}{x - 3} \right)} - 5 \sinh{\left(\frac{1}{x - 3} \right)} - 5 \cosh{\left(\frac{1}{x - 3} \right)}}{\left(x - 3\right)^{4}} 
    1                    1   
  ------               ------
  -3 + x               -3 + x
 e          (6 - 2*x)*e      
--------- - -----------------
        4               4    
(-3 + x)        (-3 + x)
−(6−2x)e1x−3(x−3)4+e1x−3(x−3)4- \frac{\left(6 - 2 x\right) e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} + \frac{e^{\frac{1}{x - 3}}}{\left(x - 3\right)^{4}} 
    /  1   \       /  1   \             /    /  1   \       /  1   \\
cosh|------| + sinh|------|   (6 - 2*x)*|cosh|------| + sinh|------||
    \-3 + x/       \-3 + x/             \    \-3 + x/       \-3 + x//
--------------------------- - ---------------------------------------
                 4                                   4               
         (-3 + x)                            (-3 + x)
−(6−2x)(sinh⁡(1x−3)+cosh⁡(1x−3))(x−3)4+sinh⁡(1x−3)+cosh⁡(1x−3)(x−3)4- \frac{\left(6 - 2 x\right) \left(\sinh{\left(\frac{1}{x - 3} \right)} + \cosh{\left(\frac{1}{x - 3} \right)}\right)}{\left(x - 3\right)^{4}} + \frac{\sinh{\left(\frac{1}{x - 3} \right)} + \cosh{\left(\frac{1}{x - 3} \right)}}{\left(x - 3\right)^{4}} 
(cosh(1/(-3 + x)) + sinh(1/(-3 + x)))/(-3 + x)^4 - (6 - 2*x)*(cosh(1/(-3 + x)) + sinh(1/(-3 + x)))/(-3 + x)^4
    © Sr Examen – Калькулятор