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Simplificación de expresiones/ Descomposición en fracciones simples/ ((z-2)/(4*(z+2)^2))/(z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z))

¿Cómo vas a descomponer esta ((z-2)/(4*(z+2)^2))/(z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
         /  z - 2   \        
         |----------|        
         |         2|        
         \4*(z + 2) /        
-----------------------------
            2                
   z       z  + 4       z    
------- - -------- - --------
2*z - 4      2        2      
          2*z  - 8   z  + 2*z
$$\frac{\frac{1}{4 \left(z + 2\right)^{2}} \left(z - 2\right)}{- \frac{z}{z^{2} + 2 z} + \left(\frac{z}{2 z - 4} - \frac{z^{2} + 4}{2 z^{2} - 8}\right)}$$ 
((z - 2)/((4*(z + 2)^2)))/(z/(2*z - 4) - (z^2 + 4)/(2*z^2 - 8) - z/(z^2 + 2*z))
Simplificación general [src] 
zoo
$$\tilde{\infty}$$ 
±oo
Respuesta numérica [src] 
0.0625*(-2.0 + z)/((1 + 0.5*z)^2*(z/(-4.0 + 2.0*z) - z/(z^2 + 2.0*z) - (4.0 + z^2)/(-8.0 + 2.0*z^2)))
0.0625*(-2.0 + z)/((1 + 0.5*z)^2*(z/(-4.0 + 2.0*z) - z/(z^2 + 2.0*z) - (4.0 + z^2)/(-8.0 + 2.0*z^2)))
Compilar la expresión [src] 
                   -2 + z                   
--------------------------------------------
           /                             2 \
         2 |   z          z         4 + z  |
4*(2 + z) *|-------- - -------- - ---------|
           |-4 + 2*z    2                 2|
           \           z  + 2*z   -8 + 2*z /
$$\frac{z - 2}{4 \left(z + 2\right)^{2} \left(- \frac{z}{z^{2} + 2 z} + \frac{z}{2 z - 4} - \frac{z^{2} + 4}{2 z^{2} - 8}\right)}$$ 
(-2 + z)/(4*(2 + z)^2*(z/(-4 + 2*z) - z/(z^2 + 2*z) - (4 + z^2)/(-8 + 2*z^2)))
Unión de expresiones racionales [src] 
                                    2 /      2\                             
                            (-2 + z) *\-4 + z /                             
----------------------------------------------------------------------------
          /        /  /      2\            /     2\\     /      2\         \
2*(2 + z)*\(2 + z)*\z*\-4 + z / - (-2 + z)*\4 + z // - 2*\-4 + z /*(-2 + z)/
$$\frac{\left(z - 2\right)^{2} \left(z^{2} - 4\right)}{2 \left(z + 2\right) \left(- 2 \left(z - 2\right) \left(z^{2} - 4\right) + \left(z + 2\right) \left(z \left(z^{2} - 4\right) - \left(z - 2\right) \left(z^{2} + 4\right)\right)\right)}$$ 
(-2 + z)^2*(-4 + z^2)/(2*(2 + z)*((2 + z)*(z*(-4 + z^2) - (-2 + z)*(4 + z^2)) - 2*(-4 + z^2)*(-2 + z)))
Combinatoria [src] 
            3
zoo*(-2 + z)
$$\tilde{\infty} \left(z - 2\right)^{3}$$ 
±oo*(-2 + z)^3
Denominador común [src] 
zoo
$$\tilde{\infty}$$ 
±oo
Parte trigonométrica [src] 
                   -2 + z                   
--------------------------------------------
           /                             2 \
         2 |   z          z         4 + z  |
4*(2 + z) *|-------- - -------- - ---------|
           |-4 + 2*z    2                 2|
           \           z  + 2*z   -8 + 2*z /
$$\frac{z - 2}{4 \left(z + 2\right)^{2} \left(- \frac{z}{z^{2} + 2 z} + \frac{z}{2 z - 4} - \frac{z^{2} + 4}{2 z^{2} - 8}\right)}$$ 
(-2 + z)/(4*(2 + z)^2*(z/(-4 + 2*z) - z/(z^2 + 2*z) - (4 + z^2)/(-8 + 2*z^2)))
Denominador racional [src] 
             2        3        4        5        6
zoo*z + zoo*z  + zoo*z  + zoo*z  + zoo*z  + zoo*z 
--------------------------------------------------
                             2                    
                    4*(2 + z)
$$\frac{\tilde{\infty} z^{6} + \tilde{\infty} z^{5} + \tilde{\infty} z^{4} + \tilde{\infty} z^{3} + \tilde{\infty} z^{2} + \tilde{\infty} z}{4 \left(z + 2\right)^{2}}$$ 
(±oo*z + ±oo*z^2 + ±oo*z^3 + ±oo*z^4 + ±oo*z^5 + ±oo*z^6)/(4*(2 + z)^2)
Potencias [src] 
                   -2 + z                   
--------------------------------------------
           /                             2 \
         2 |   z          z         4 + z  |
4*(2 + z) *|-------- - -------- - ---------|
           |-4 + 2*z    2                 2|
           \           z  + 2*z   -8 + 2*z /
$$\frac{z - 2}{4 \left(z + 2\right)^{2} \left(- \frac{z}{z^{2} + 2 z} + \frac{z}{2 z - 4} - \frac{z^{2} + 4}{2 z^{2} - 8}\right)}$$ 
                   1   z                  
                 - - + -                  
                   2   4                  
------------------------------------------
         /                  2            \
       2 |   z        -4 - z        z    |
(2 + z) *|-------- + --------- - --------|
         |-4 + 2*z           2    2      |
         \           -8 + 2*z    z  + 2*z/
$$\frac{\frac{z}{4} - \frac{1}{2}}{\left(z + 2\right)^{2} \left(- \frac{z}{z^{2} + 2 z} + \frac{z}{2 z - 4} + \frac{- z^{2} - 4}{2 z^{2} - 8}\right)}$$ 
(-1/2 + z/4)/((2 + z)^2*(z/(-4 + 2*z) + (-4 - z^2)/(-8 + 2*z^2) - z/(z^2 + 2*z)))
Abrimos la expresión [src] 
                  z - 2                   
------------------------------------------
           /            2                \
         2 |   z       z  + 4       z    |
4*(z + 2) *|------- - -------- - --------|
           |2*z - 4      2        2      |
           \          2*z  - 8   z  + 2*z/
$$\frac{z - 2}{4 \left(z + 2\right)^{2} \left(- \frac{z}{z^{2} + 2 z} + \left(\frac{z}{2 z - 4} - \frac{z^{2} + 4}{2 z^{2} - 8}\right)\right)}$$ 
(z - 2)/(4*(z + 2)^2*(z/(2*z - 4) - (z^2 + 4)/(2*z^2 - 8) - z/(z^2 + 2*z)))
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