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Simplificación de expresiones/ Descomposición en fracciones simples/ (y/(4*y+16)+(y^2+16)/(4*y^2-64)-(4/(y^2-4*y)))/(3*y^2-24*y+48)/(y+4)

¿Cómo vas a descomponer esta (y/(4*y+16)+(y^2+16)/(4*y^2-64)-(4/(y^2-4*y)))/(3*y^2-24*y+48)/(y+4) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
/             2                 \
|   y        y  + 16       4    |
|-------- + --------- - --------|
|4*y + 16      2         2      |
|           4*y  - 64   y  - 4*y|
|-------------------------------|
|           2                   |
\        3*y  - 24*y + 48       /
---------------------------------
              y + 4
1(3y2−24y)+48((y4y+16+y2+164y2−64)−4y2−4y)y+4\frac{\frac{1}{\left(3 y^{2} - 24 y\right) + 48} \left(\left(\frac{y}{4 y + 16} + \frac{y^{2} + 16}{4 y^{2} - 64}\right) - \frac{4}{y^{2} - 4 y}\right)}{y + 4} 
((y/(4*y + 16) + (y^2 + 16)/(4*y^2 - 64) - 4/(y^2 - 4*y))/(3*y^2 - 24*y + 48))/(y + 4)
Descomposición de una fracción [src] 
-1/(96*(4 + y)^2) - 1/(256*(-4 + y)) - 1/(768*(4 + y)) + 1/(48*(-4 + y)^2) + 1/(192*y)
−1768(y+4)−196(y+4)2−1256(y−4)+148(y−4)2+1192y- \frac{1}{768 \left(y + 4\right)} - \frac{1}{96 \left(y + 4\right)^{2}} - \frac{1}{256 \left(y - 4\right)} + \frac{1}{48 \left(y - 4\right)^{2}} + \frac{1}{192 y} 
       1             1              1             1           1  
- ----------- - ------------ - ----------- + ------------ + -----
            2   256*(-4 + y)   768*(4 + y)              2   192*y
  96*(4 + y)                                 48*(-4 + y)
Simplificación general [src] 
          2           
     8 + y  + 2*y     
----------------------
    /       4       2\
6*y*\256 + y  - 32*y /
y2+2y+86y(y4−32y2+256)\frac{y^{2} + 2 y + 8}{6 y \left(y^{4} - 32 y^{2} + 256\right)} 
(8 + y^2 + 2*y)/(6*y*(256 + y^4 - 32*y^2))
Parte trigonométrica [src] 
                               2  
     4          y        16 + y   
- -------- + -------- + ----------
   2         16 + 4*y            2
  y  - 4*y              -64 + 4*y 
----------------------------------
            /               2\    
    (4 + y)*\48 - 24*y + 3*y /
y4y+16+y2+164y2−64−4y2−4y(y+4)(3y2−24y+48)\frac{\frac{y}{4 y + 16} + \frac{y^{2} + 16}{4 y^{2} - 64} - \frac{4}{y^{2} - 4 y}}{\left(y + 4\right) \left(3 y^{2} - 24 y + 48\right)} 
(-4/(y^2 - 4*y) + y/(16 + 4*y) + (16 + y^2)/(-64 + 4*y^2))/((4 + y)*(48 - 24*y + 3*y^2))
Denominador racional [src] 
/ 2      \ /  /         2\   /      2\           \     /         2\           
\y  - 4*y/*\y*\-64 + 4*y / + \16 + y /*(16 + 4*y)/ - 4*\-64 + 4*y /*(16 + 4*y)
------------------------------------------------------------------------------
        /         2\                    / 2      \ /               2\         
        \-64 + 4*y /*(4 + y)*(16 + 4*y)*\y  - 4*y/*\48 - 24*y + 3*y /
−4(4y+16)(4y2−64)+(y2−4y)(y(4y2−64)+(4y+16)(y2+16))(y+4)(4y+16)(y2−4y)(4y2−64)(3y2−24y+48)\frac{- 4 \left(4 y + 16\right) \left(4 y^{2} - 64\right) + \left(y^{2} - 4 y\right) \left(y \left(4 y^{2} - 64\right) + \left(4 y + 16\right) \left(y^{2} + 16\right)\right)}{\left(y + 4\right) \left(4 y + 16\right) \left(y^{2} - 4 y\right) \left(4 y^{2} - 64\right) \left(3 y^{2} - 24 y + 48\right)} 
((y^2 - 4*y)*(y*(-64 + 4*y^2) + (16 + y^2)*(16 + 4*y)) - 4*(-64 + 4*y^2)*(16 + 4*y))/((-64 + 4*y^2)*(4 + y)*(16 + 4*y)*(y^2 - 4*y)*(48 - 24*y + 3*y^2))
Combinatoria [src] 
          2           
     8 + y  + 2*y     
----------------------
            2        2
6*y*(-4 + y) *(4 + y)
y2+2y+86y(y−4)2(y+4)2\frac{y^{2} + 2 y + 8}{6 y \left(y - 4\right)^{2} \left(y + 4\right)^{2}} 
(8 + y^2 + 2*y)/(6*y*(-4 + y)^2*(4 + y)^2)
Potencias [src] 
                               2  
     4          y        16 + y   
- -------- + -------- + ----------
   2         16 + 4*y            2
  y  - 4*y              -64 + 4*y 
----------------------------------
            /               2\    
    (4 + y)*\48 - 24*y + 3*y /
y4y+16+y2+164y2−64−4y2−4y(y+4)(3y2−24y+48)\frac{\frac{y}{4 y + 16} + \frac{y^{2} + 16}{4 y^{2} - 64} - \frac{4}{y^{2} - 4 y}}{\left(y + 4\right) \left(3 y^{2} - 24 y + 48\right)} 
(-4/(y^2 - 4*y) + y/(16 + 4*y) + (16 + y^2)/(-64 + 4*y^2))/((4 + y)*(48 - 24*y + 3*y^2))
Unión de expresiones racionales [src] 
     /       2\                      /  /       2\           /      2\\
- 16*\-16 + y /*(4 + y) + y*(-4 + y)*\y*\-16 + y / + (4 + y)*\16 + y //
-----------------------------------------------------------------------
               /       2\                 2                            
          12*y*\-16 + y /*(-4 + y)*(4 + y) *(16 + y*(-8 + y))
y(y−4)(y(y2−16)+(y+4)(y2+16))−16(y+4)(y2−16)12y(y−4)(y+4)2(y2−16)(y(y−8)+16)\frac{y \left(y - 4\right) \left(y \left(y^{2} - 16\right) + \left(y + 4\right) \left(y^{2} + 16\right)\right) - 16 \left(y + 4\right) \left(y^{2} - 16\right)}{12 y \left(y - 4\right) \left(y + 4\right)^{2} \left(y^{2} - 16\right) \left(y \left(y - 8\right) + 16\right)} 
(-16*(-16 + y^2)*(4 + y) + y*(-4 + y)*(y*(-16 + y^2) + (4 + y)*(16 + y^2)))/(12*y*(-16 + y^2)*(-4 + y)*(4 + y)^2*(16 + y*(-8 + y)))
Denominador común [src] 
           2            
      8 + y  + 2*y      
------------------------
       3      5         
- 192*y  + 6*y  + 1536*y
y2+2y+86y5−192y3+1536y\frac{y^{2} + 2 y + 8}{6 y^{5} - 192 y^{3} + 1536 y} 
(8 + y^2 + 2*y)/(-192*y^3 + 6*y^5 + 1536*y)
Compilar la expresión [src] 
                               2  
     4          y        16 + y   
- -------- + -------- + ----------
   2         16 + 4*y            2
  y  - 4*y              -64 + 4*y 
----------------------------------
            /               2\    
    (4 + y)*\48 - 24*y + 3*y /
y4y+16+y2+164y2−64−4y2−4y(y+4)(3y2−24y+48)\frac{\frac{y}{4 y + 16} + \frac{y^{2} + 16}{4 y^{2} - 64} - \frac{4}{y^{2} - 4 y}}{\left(y + 4\right) \left(3 y^{2} - 24 y + 48\right)} 
(-4/(y^2 - 4*y) + y/(16 + 4*y) + (16 + y^2)/(-64 + 4*y^2))/((4 + y)*(48 - 24*y + 3*y^2))
Respuesta numérica [src] 
(-4.0/(y^2 - 4.0*y) + y/(16.0 + 4.0*y) + (16.0 + y^2)/(-64.0 + 4.0*y^2))/((4.0 + y)*(48.0 + 3.0*y^2 - 24.0*y))
(-4.0/(y^2 - 4.0*y) + y/(16.0 + 4.0*y) + (16.0 + y^2)/(-64.0 + 4.0*y^2))/((4.0 + y)*(48.0 + 3.0*y^2 - 24.0*y))
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