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Simplificación de expresiones/ Descomposición en fracciones simples/ ((z-2)/(4*z^2+16*z+16))/((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+16*z+16))/((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  + 16*z + 16/     
-----------------------------
            2                
   z       z  + 4       z    
------- - -------- - --------
2*z - 4      2        2      
          2*z  - 8   z  + 2*z
$$\frac{\left(z - 2\right) \frac{1}{\left(4 z^{2} + 16 z\right) + 16}}{- \frac{z}{z^{2} + 2 z} + \left(\frac{z}{2 z - 4} - \frac{z^{2} + 4}{2 z^{2} - 8}\right)}$$ 
((z - 2)/(4*z^2 + 16*z + 16))/(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] 
(-2.0 + z)/((16.0 + 4.0*z^2 + 16.0*z)*(z/(-4.0 + 2.0*z) - z/(z^2 + 2.0*z) - (4.0 + z^2)/(-8.0 + 2.0*z^2)))
(-2.0 + z)/((16.0 + 4.0*z^2 + 16.0*z)*(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  |
\16 + 4*z  + 16*z/*|-------- - -------- - ---------|
                   |-4 + 2*z    2                 2|
                   \           z  + 2*z   -8 + 2*z /
$$\frac{z - 2}{\left(4 z^{2} + 16 z + 16\right) \left(- \frac{z}{z^{2} + 2 z} + \frac{z}{2 z - 4} - \frac{z^{2} + 4}{2 z^{2} - 8}\right)}$$ 
(-2 + z)/((16 + 4*z^2 + 16*z)*(z/(-4 + 2*z) - z/(z^2 + 2*z) - (4 + z^2)/(-8 + 2*z^2)))
Denominador común [src] 
zoo
$$\tilde{\infty}$$ 
±oo
Parte trigonométrica [src] 
                       -2 + z                       
----------------------------------------------------
                   /                             2 \
/        2       \ |   z          z         4 + z  |
\16 + 4*z  + 16*z/*|-------- - -------- - ---------|
                   |-4 + 2*z    2                 2|
                   \           z  + 2*z   -8 + 2*z /
$$\frac{z - 2}{\left(4 z^{2} + 16 z + 16\right) \left(- \frac{z}{z^{2} + 2 z} + \frac{z}{2 z - 4} - \frac{z^{2} + 4}{2 z^{2} - 8}\right)}$$ 
(-2 + z)/((16 + 4*z^2 + 16*z)*(z/(-4 + 2*z) - z/(z^2 + 2*z) - (4 + z^2)/(-8 + 2*z^2)))
Potencias [src] 
                       -2 + z                       
----------------------------------------------------
                   /                             2 \
/        2       \ |   z          z         4 + z  |
\16 + 4*z  + 16*z/*|-------- - -------- - ---------|
                   |-4 + 2*z    2                 2|
                   \           z  + 2*z   -8 + 2*z /
$$\frac{z - 2}{\left(4 z^{2} + 16 z + 16\right) \left(- \frac{z}{z^{2} + 2 z} + \frac{z}{2 z - 4} - \frac{z^{2} + 4}{2 z^{2} - 8}\right)}$$ 
                       -2 + z                       
----------------------------------------------------
                   /                  2            \
/        2       \ |   z        -4 - z        z    |
\16 + 4*z  + 16*z/*|-------- + --------- - --------|
                   |-4 + 2*z           2    2      |
                   \           -8 + 2*z    z  + 2*z/
$$\frac{z - 2}{\left(4 z^{2} + 16 z + 16\right) \left(- \frac{z}{z^{2} + 2 z} + \frac{z}{2 z - 4} + \frac{- z^{2} - 4}{2 z^{2} - 8}\right)}$$ 
(-2 + z)/((16 + 4*z^2 + 16*z)*(z/(-4 + 2*z) + (-4 - z^2)/(-8 + 2*z^2) - z/(z^2 + 2*z)))
Unión de expresiones racionales [src] 
                                    2 /      2\                                     
                            (-2 + z) *\-4 + z /*(2 + z)                             
------------------------------------------------------------------------------------
                  /        /  /      2\            /     2\\     /      2\         \
2*(4 + z*(4 + z))*\(2 + z)*\z*\-4 + z / - (-2 + z)*\4 + z // - 2*\-4 + z /*(-2 + z)/
$$\frac{\left(z - 2\right)^{2} \left(z + 2\right) \left(z^{2} - 4\right)}{2 \left(z \left(z + 4\right) + 4\right) \left(- 2 \left(z - 2\right) \left(z^{2} - 4\right) + \left(z + 2\right) \left(z \left(z^{2} - 4\right) - \left(z - 2\right) \left(z^{2} + 4\right)\right)\right)}$$ 
(-2 + z)^2*(-4 + z^2)*(2 + z)/(2*(4 + z*(4 + z))*((2 + z)*(z*(-4 + z^2) - (-2 + z)*(4 + z^2)) - 2*(-4 + z^2)*(-2 + z)))
Denominador racional [src] 
  /         2    3    4    5\    
z*\1 + z + z  + z  + z  + z /*zoo
---------------------------------
                2                
           4 + z  + 4*z
$$\frac{\tilde{\infty} z \left(z^{5} + z^{4} + z^{3} + z^{2} + z + 1\right)}{z^{2} + 4 z + 4}$$ 
z*(1 + z + z^2 + z^3 + z^4 + z^5)*±oo/(4 + z^2 + 4*z)
Combinatoria [src] 
            3
zoo*(-2 + z)
$$\tilde{\infty} \left(z - 2\right)^{3}$$ 
±oo*(-2 + z)^3
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