Sr Examen

Otras calculadoras

¿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       
$$\left(16 z + \left(- \frac{z^{2}}{2} + z\right)\right) + \frac{16}{2 z + \left(\left(\left(2 z^{2} + \left(- z^{2} + \left(z \frac{z}{2} - 4\right)\right)\right) - 8\right) - \frac{2}{z^{2}}\right)}$$
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)
$$- \frac{z^{2}}{2} + \frac{32 z^{2}}{3 z^{4} + 4 z^{3} - 24 z^{2} - 4} + 17 z$$
        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//         
$$\frac{z \left(64 z + \left(34 - z\right) \left(z^{2} \left(3 z^{2} + 4 z - 24\right) - 4\right)\right)}{2 \left(z^{2} \left(3 z^{2} + 4 z - 24\right) - 4\right)}$$
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                          
$$- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}}$$
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 
$$- \frac{z^{2}}{2} + \frac{32 z^{2}}{3 z^{4} + 4 z^{3} - 24 z^{2} - 4} + 17 z$$
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                          
$$- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}}$$
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             
$$- \frac{z \left(3 z^{5} - 98 z^{4} - 160 z^{3} + 816 z^{2} - 68 z + 136\right)}{6 z^{4} + 8 z^{3} - 48 z^{2} - 8}$$
-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                          
$$- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}}$$
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 //         
$$\frac{z \left(64 z + \left(34 - z\right) \left(4 z^{3} + 3 z^{2} \left(z^{2} - 8\right) - 4\right)\right)}{2 \left(4 z^{3} + 3 z^{2} \left(z^{2} - 8\right) - 4\right)}$$
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 /          
$$- \frac{z \left(3 z^{5} - 98 z^{4} - 160 z^{3} + 816 z^{2} - 68 z + 136\right)}{2 \left(3 z^{4} + 4 z^{3} - 24 z^{2} - 4\right)}$$
-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))