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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^2-8-2/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^2-8-2/z^2+2*z) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     2                                            
    z                           16                
z - -- + 16*z + ----------------------------------
    2           z          2      2       2       
                -*z - 4 - z  + 2*z  - 8 - -- + 2*z
                2                          2      
                                          z
(16z+(−z22+z))+162z+(((2z2+(−z2+(zz2−4)))−8)−2z2)\left(16 z + \left(- \frac{z^{2}}{2} + z\right)\right) + \frac{16}{2 z + \left(\left(\left(2 z^{2} + \left(- z^{2} + \left(z \frac{z}{2} - 4\right)\right)\right) - 8\right) - \frac{2}{z^{2}}\right)} 
z - z^2/2 + 16*z + 16/((z/2)*z - 4 - z^2 + 2*z^2 - 8 - 2/z^2 + 2*z)
Descomposición de una fracción [src] 
17*z - z^2/2 + 32*z^2/(-4 - 24*z^2 + 3*z^4 + 4*z^3)
−z22+32z23z4+4z3−24z2−4+17z- \frac{z^{2}}{2} + \frac{32 z^{2}}{3 z^{4} + 4 z^{3} - 24 z^{2} - 4} + 17 z 
        2                2          
       z             32*z           
17*z - -- + ------------------------
       2             2      4      3
            -4 - 24*z  + 3*z  + 4*z
Simplificación general [src] 
  /       /      2 /         2      \\         \
z*\64*z + \-4 + z *\-24 + 3*z  + 4*z//*(34 - z)/
------------------------------------------------
           /      2 /         2      \\         
         2*\-4 + z *\-24 + 3*z  + 4*z//
z(64z+(34−z)(z2(3z2+4z−24)−4))2(z2(3z2+4z−24)−4)\frac{z \left(64 z + \left(34 - z\right) \left(z^{2} \left(3 z^{2} + 4 z - 24\right) - 4\right)\right)}{2 \left(z^{2} \left(3 z^{2} + 4 z - 24\right) - 4\right)} 
z*(64*z + (-4 + z^2*(-24 + 3*z^2 + 4*z))*(34 - z))/(2*(-4 + z^2*(-24 + 3*z^2 + 4*z)))
Respuesta numérica [src] 
16.0/(-12.0 + 2.0*z + 1.5*z^2 - 2.0/z^2) + 17.0*z - 0.5*z^2
16.0/(-12.0 + 2.0*z + 1.5*z^2 - 2.0/z^2) + 17.0*z - 0.5*z^2
Parte trigonométrica [src] 
                                2
          16                   z 
--------------------- + 17*z - --
                    2          2 
      2          3*z             
-12 - -- + 2*z + ----            
       2          2              
      z
−z22+17z+163z22+2z−12−2z2- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}} 
16/(-12 - 2/z^2 + 2*z + 3*z^2/2) + 17*z - z^2/2
Denominador común [src] 
        2                2          
       z             32*z           
17*z - -- + ------------------------
       2             2      4      3
            -4 - 24*z  + 3*z  + 4*z
−z22+32z23z4+4z3−24z2−4+17z- \frac{z^{2}}{2} + \frac{32 z^{2}}{3 z^{4} + 4 z^{3} - 24 z^{2} - 4} + 17 z 
17*z - z^2/2 + 32*z^2/(-4 - 24*z^2 + 3*z^4 + 4*z^3)
Compilar la expresión [src] 
                                2
          16                   z 
--------------------- + 17*z - --
                    2          2 
      2          3*z             
-12 - -- + 2*z + ----            
       2          2              
      z
−z22+17z+163z22+2z−12−2z2- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}} 
16/(-12 - 2/z^2 + 2*z + 3*z^2/2) + 17*z - z^2/2
Denominador racional [src] 
   /           3       4             5        2\ 
-z*\136 - 160*z  - 98*z  - 68*z + 3*z  + 816*z / 
-------------------------------------------------
                      2      4      3            
             -8 - 48*z  + 6*z  + 8*z
−z(3z5−98z4−160z3+816z2−68z+136)6z4+8z3−48z2−8- \frac{z \left(3 z^{5} - 98 z^{4} - 160 z^{3} + 816 z^{2} - 68 z + 136\right)}{6 z^{4} + 8 z^{3} - 48 z^{2} - 8} 
-z*(136 - 160*z^3 - 98*z^4 - 68*z + 3*z^5 + 816*z^2)/(-8 - 48*z^2 + 6*z^4 + 8*z^3)
Potencias [src] 
                                2
          16                   z 
--------------------- + 17*z - --
                    2          2 
      2          3*z             
-12 - -- + 2*z + ----            
       2          2              
      z
−z22+17z+163z22+2z−12−2z2- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}} 
16/(-12 - 2/z^2 + 2*z + 3*z^2/2) + 17*z - z^2/2
Unión de expresiones racionales [src] 
  /                /        3      2 /      2\\\
z*\64*z + (34 - z)*\-4 + 4*z  + 3*z *\-8 + z ///
------------------------------------------------
           /        3      2 /      2\\         
         2*\-4 + 4*z  + 3*z *\-8 + z //
z(64z+(34−z)(4z3+3z2(z2−8)−4))2(4z3+3z2(z2−8)−4)\frac{z \left(64 z + \left(34 - z\right) \left(4 z^{3} + 3 z^{2} \left(z^{2} - 8\right) - 4\right)\right)}{2 \left(4 z^{3} + 3 z^{2} \left(z^{2} - 8\right) - 4\right)} 
z*(64*z + (34 - z)*(-4 + 4*z^3 + 3*z^2*(-8 + z^2)))/(2*(-4 + 4*z^3 + 3*z^2*(-8 + z^2)))
Combinatoria [src] 
   /           3       4             5        2\ 
-z*\136 - 160*z  - 98*z  - 68*z + 3*z  + 816*z / 
-------------------------------------------------
             /         2      4      3\          
           2*\-4 - 24*z  + 3*z  + 4*z /
−z(3z5−98z4−160z3+816z2−68z+136)2(3z4+4z3−24z2−4)- \frac{z \left(3 z^{5} - 98 z^{4} - 160 z^{3} + 816 z^{2} - 68 z + 136\right)}{2 \left(3 z^{4} + 4 z^{3} - 24 z^{2} - 4\right)} 
-z*(136 - 160*z^3 - 98*z^4 - 68*z + 3*z^5 + 816*z^2)/(2*(-4 - 24*z^2 + 3*z^4 + 4*z^3))
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