Sr Examen

Otras calculadoras

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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    z           z  
   e         3*e   
-------- - --------
       3          4
(z - 1)    (z - 1)
−3ez(z−1)4+ez(z−1)3- \frac{3 e^{z}}{\left(z - 1\right)^{4}} + \frac{e^{z}}{\left(z - 1\right)^{3}} 
exp(z)/(z - 1)^3 - 3*exp(z)/(z - 1)^4
Simplificación general [src] 
          z
(-4 + z)*e 
-----------
         4 
 (-1 + z)
(z−4)ez(z−1)4\frac{\left(z - 4\right) e^{z}}{\left(z - 1\right)^{4}} 
(-4 + z)*exp(z)/(-1 + z)^4
Respuesta numérica [src] 
exp(z)/(-1.0 + z)^3 - 3.0*exp(z)/(-1.0 + z)^4
exp(z)/(-1.0 + z)^3 - 3.0*exp(z)/(-1.0 + z)^4
Denominador racional [src] 
        4  z             3  z
(-1 + z) *e  - 3*(-1 + z) *e 
-----------------------------
                  7          
          (-1 + z)
(z−1)4ez−3(z−1)3ez(z−1)7\frac{\left(z - 1\right)^{4} e^{z} - 3 \left(z - 1\right)^{3} e^{z}}{\left(z - 1\right)^{7}} 
((-1 + z)^4*exp(z) - 3*(-1 + z)^3*exp(z))/(-1 + z)^7
Compilar la expresión [src] 
     z            z  
    e          3*e   
--------- - ---------
        3           4
(-1 + z)    (-1 + z)
ez(z−1)3−3ez(z−1)4\frac{e^{z}}{\left(z - 1\right)^{3}} - \frac{3 e^{z}}{\left(z - 1\right)^{4}} 
exp(z)/(-1 + z)^3 - 3*exp(z)/(-1 + z)^4
Combinatoria [src] 
          z
(-4 + z)*e 
-----------
         4 
 (-1 + z)
(z−4)ez(z−1)4\frac{\left(z - 4\right) e^{z}}{\left(z - 1\right)^{4}} 
(-4 + z)*exp(z)/(-1 + z)^4
Unión de expresiones racionales [src] 
          z
(-4 + z)*e 
-----------
         4 
 (-1 + z)
(z−4)ez(z−1)4\frac{\left(z - 4\right) e^{z}}{\left(z - 1\right)^{4}} 
(-4 + z)*exp(z)/(-1 + z)^4
Potencias [src] 
     z            z  
    e          3*e   
--------- - ---------
        3           4
(-1 + z)    (-1 + z)
ez(z−1)3−3ez(z−1)4\frac{e^{z}}{\left(z - 1\right)^{3}} - \frac{3 e^{z}}{\left(z - 1\right)^{4}} 
exp(z)/(-1 + z)^3 - 3*exp(z)/(-1 + z)^4
Parte trigonométrica [src] 
cosh(z) + sinh(z)   3*cosh(z) + 3*sinh(z)
----------------- - ---------------------
            3                     4      
    (-1 + z)              (-1 + z)
sinh⁡(z)+cosh⁡(z)(z−1)3−3sinh⁡(z)+3cosh⁡(z)(z−1)4\frac{\sinh{\left(z \right)} + \cosh{\left(z \right)}}{\left(z - 1\right)^{3}} - \frac{3 \sinh{\left(z \right)} + 3 \cosh{\left(z \right)}}{\left(z - 1\right)^{4}} 
-4*cosh(z) - 4*sinh(z) + z*cosh(z) + z*sinh(z)
----------------------------------------------
                          4                   
                  (-1 + z)
zsinh⁡(z)+zcosh⁡(z)−4sinh⁡(z)−4cosh⁡(z)(z−1)4\frac{z \sinh{\left(z \right)} + z \cosh{\left(z \right)} - 4 \sinh{\left(z \right)} - 4 \cosh{\left(z \right)}}{\left(z - 1\right)^{4}} 
     z            z  
    e          3*e   
--------- - ---------
        3           4
(-1 + z)    (-1 + z)
ez(z−1)3−3ez(z−1)4\frac{e^{z}}{\left(z - 1\right)^{3}} - \frac{3 e^{z}}{\left(z - 1\right)^{4}} 
cosh(z) + sinh(z)   3*(cosh(z) + sinh(z))
----------------- - ---------------------
            3                     4      
    (-1 + z)              (-1 + z)
sinh⁡(z)+cosh⁡(z)(z−1)3−3(sinh⁡(z)+cosh⁡(z))(z−1)4\frac{\sinh{\left(z \right)} + \cosh{\left(z \right)}}{\left(z - 1\right)^{3}} - \frac{3 \left(\sinh{\left(z \right)} + \cosh{\left(z \right)}\right)}{\left(z - 1\right)^{4}} 
(cosh(z) + sinh(z))/(-1 + z)^3 - 3*(cosh(z) + sinh(z))/(-1 + z)^4
Denominador común [src] 
           z      z       
      - 4*e  + z*e        
--------------------------
     4            3      2
1 + z  - 4*z - 4*z  + 6*z
zez−4ezz4−4z3+6z2−4z+1\frac{z e^{z} - 4 e^{z}}{z^{4} - 4 z^{3} + 6 z^{2} - 4 z + 1} 
(-4*exp(z) + z*exp(z))/(1 + z^4 - 4*z - 4*z^3 + 6*z^2)
    © Sr Examen – Калькулятор