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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
               /   a - 2    \       
               |------------|       
               | 2          |       
  2            \a  + 4*a + 4/       
----- + ----------------------------
a + 2               2               
           a       a  + 4      2    
        ------- + ------- - --------
        2*a - 4   8 - 2*a          2
                            2*a + a
(a−2)1(a2+4a)+4(a2a−4+a2+48−2a)−2a2+2a+2a+2\frac{\left(a - 2\right) \frac{1}{\left(a^{2} + 4 a\right) + 4}}{\left(\frac{a}{2 a - 4} + \frac{a^{2} + 4}{8 - 2 a}\right) - \frac{2}{a^{2} + 2 a}} + \frac{2}{a + 2} 
2/(a + 2) + ((a - 2)/(a^2 + 4*a + 4))/(a/(2*a - 4) + (a^2 + 4)/(8 - 2*a) - 2/(2*a + a^2))
Descomposición de una fracción [src] 
-2/(2 + a) + 2*(32 - 48*a - 7*a^3 + 2*a^4 + 26*a^2)/(32 + a^5 - a^4 - 40*a + 2*a^3 + 12*a^2)
2(2a4−7a3+26a2−48a+32)a5−a4+2a3+12a2−40a+32−2a+2\frac{2 \left(2 a^{4} - 7 a^{3} + 26 a^{2} - 48 a + 32\right)}{a^{5} - a^{4} + 2 a^{3} + 12 a^{2} - 40 a + 32} - \frac{2}{a + 2} 
            /               3      4       2\
    2     2*\32 - 48*a - 7*a  + 2*a  + 26*a /
- ----- + -----------------------------------
  2 + a          5    4             3       2
           32 + a  - a  - 40*a + 2*a  + 12*a
Simplificación general [src] 
  /      5             2      4       3\
2*\32 + a  - 24*a - 8*a  - 2*a  + 10*a /
----------------------------------------
        5    6              2       3   
  64 + a  + a  - 48*a - 16*a  + 16*a
2(a5−2a4+10a3−8a2−24a+32)a6+a5+16a3−16a2−48a+64\frac{2 \left(a^{5} - 2 a^{4} + 10 a^{3} - 8 a^{2} - 24 a + 32\right)}{a^{6} + a^{5} + 16 a^{3} - 16 a^{2} - 48 a + 64} 
2*(32 + a^5 - 24*a - 8*a^2 - 2*a^4 + 10*a^3)/(64 + a^5 + a^6 - 48*a - 16*a^2 + 16*a^3)
Parte trigonométrica [src] 
  2                          -2 + a                     
----- + ------------------------------------------------
2 + a                  /                              2\
        /     2      \ |     2          a        4 + a |
        \4 + a  + 4*a/*|- -------- + -------- + -------|
                       |   2         -4 + 2*a   8 - 2*a|
                       \  a  + 2*a                     /
a−2(a2+4a+4)(a2a−4−2a2+2a+a2+48−2a)+2a+2\frac{a - 2}{\left(a^{2} + 4 a + 4\right) \left(\frac{a}{2 a - 4} - \frac{2}{a^{2} + 2 a} + \frac{a^{2} + 4}{8 - 2 a}\right)} + \frac{2}{a + 2} 
2/(2 + a) + (-2 + a)/((4 + a^2 + 4*a)*(-2/(a^2 + 2*a) + a/(-4 + 2*a) + (4 + a^2)/(8 - 2*a)))
Denominador común [src] 
                2      4      5       3
64 - 48*a - 16*a  - 4*a  + 2*a  + 20*a 
---------------------------------------
        5    6              2       3  
  64 + a  + a  - 48*a - 16*a  + 16*a
2a5−4a4+20a3−16a2−48a+64a6+a5+16a3−16a2−48a+64\frac{2 a^{5} - 4 a^{4} + 20 a^{3} - 16 a^{2} - 48 a + 64}{a^{6} + a^{5} + 16 a^{3} - 16 a^{2} - 48 a + 64} 
(64 - 48*a - 16*a^2 - 4*a^4 + 2*a^5 + 20*a^3)/(64 + a^5 + a^6 - 48*a - 16*a^2 + 16*a^3)
Denominador racional [src] 
              2       3      7      6       5       4          
   512 - 384*a  - 64*a  + 4*a  + 8*a  + 24*a  + 96*a  + 128*a  
---------------------------------------------------------------
        /     2      \ /               4      5      3       2\
(2 + a)*\4 + a  + 4*a/*\64 - 80*a - 2*a  + 2*a  + 4*a  + 24*a /
4a7+8a6+24a5+96a4−64a3−384a2+128a+512(a+2)(a2+4a+4)(2a5−2a4+4a3+24a2−80a+64)\frac{4 a^{7} + 8 a^{6} + 24 a^{5} + 96 a^{4} - 64 a^{3} - 384 a^{2} + 128 a + 512}{\left(a + 2\right) \left(a^{2} + 4 a + 4\right) \left(2 a^{5} - 2 a^{4} + 4 a^{3} + 24 a^{2} - 80 a + 64\right)} 
(512 - 384*a^2 - 64*a^3 + 4*a^7 + 8*a^6 + 24*a^5 + 96*a^4 + 128*a)/((2 + a)*(4 + a^2 + 4*a)*(64 - 80*a - 2*a^4 + 2*a^5 + 4*a^3 + 24*a^2))
Unión de expresiones racionales [src] 
  /                /                                /                     /     2\\\             2        2        \
2*\(4 + a*(4 + a))*\-4*(-2 + a)*(4 - a) + a*(2 + a)*\a*(4 - a) + (-2 + a)*\4 + a /// + a*(-2 + a) *(2 + a) *(4 - a)/
--------------------------------------------------------------------------------------------------------------------
                                     /                                /                     /     2\\\              
             (2 + a)*(4 + a*(4 + a))*\-4*(-2 + a)*(4 - a) + a*(2 + a)*\a*(4 - a) + (-2 + a)*\4 + a ///
2(a(4−a)(a−2)2(a+2)2+(a(a+4)+4)(a(a+2)(a(4−a)+(a−2)(a2+4))−4(4−a)(a−2)))(a+2)(a(a+4)+4)(a(a+2)(a(4−a)+(a−2)(a2+4))−4(4−a)(a−2))\frac{2 \left(a \left(4 - a\right) \left(a - 2\right)^{2} \left(a + 2\right)^{2} + \left(a \left(a + 4\right) + 4\right) \left(a \left(a + 2\right) \left(a \left(4 - a\right) + \left(a - 2\right) \left(a^{2} + 4\right)\right) - 4 \left(4 - a\right) \left(a - 2\right)\right)\right)}{\left(a + 2\right) \left(a \left(a + 4\right) + 4\right) \left(a \left(a + 2\right) \left(a \left(4 - a\right) + \left(a - 2\right) \left(a^{2} + 4\right)\right) - 4 \left(4 - a\right) \left(a - 2\right)\right)} 
2*((4 + a*(4 + a))*(-4*(-2 + a)*(4 - a) + a*(2 + a)*(a*(4 - a) + (-2 + a)*(4 + a^2))) + a*(-2 + a)^2*(2 + a)^2*(4 - a))/((2 + a)*(4 + a*(4 + a))*(-4*(-2 + a)*(4 - a) + a*(2 + a)*(a*(4 - a) + (-2 + a)*(4 + a^2))))
Respuesta numérica [src] 
2.0/(2.0 + a) + (-2.0 + a)/((4.0 + a^2 + 4.0*a)*(-2.0/(a^2 + 2.0*a) + a/(-4.0 + 2.0*a) + (4.0 + a^2)/(8.0 - 2.0*a)))
2.0/(2.0 + a) + (-2.0 + a)/((4.0 + a^2 + 4.0*a)*(-2.0/(a^2 + 2.0*a) + a/(-4.0 + 2.0*a) + (4.0 + a^2)/(8.0 - 2.0*a)))
Compilar la expresión [src] 
  2                          -2 + a                     
----- + ------------------------------------------------
2 + a                  /                              2\
        /     2      \ |     2          a        4 + a |
        \4 + a  + 4*a/*|- -------- + -------- + -------|
                       |   2         -4 + 2*a   8 - 2*a|
                       \  a  + 2*a                     /
a−2(a2+4a+4)(a2a−4−2a2+2a+a2+48−2a)+2a+2\frac{a - 2}{\left(a^{2} + 4 a + 4\right) \left(\frac{a}{2 a - 4} - \frac{2}{a^{2} + 2 a} + \frac{a^{2} + 4}{8 - 2 a}\right)} + \frac{2}{a + 2} 
2/(2 + a) + (-2 + a)/((4 + a^2 + 4*a)*(-2/(a^2 + 2*a) + a/(-4 + 2*a) + (4 + a^2)/(8 - 2*a)))
Potencias [src] 
  2                          -2 + a                     
----- + ------------------------------------------------
2 + a                  /                              2\
        /     2      \ |     2          a        4 + a |
        \4 + a  + 4*a/*|- -------- + -------- + -------|
                       |   2         -4 + 2*a   8 - 2*a|
                       \  a  + 2*a                     /
a−2(a2+4a+4)(a2a−4−2a2+2a+a2+48−2a)+2a+2\frac{a - 2}{\left(a^{2} + 4 a + 4\right) \left(\frac{a}{2 a - 4} - \frac{2}{a^{2} + 2 a} + \frac{a^{2} + 4}{8 - 2 a}\right)} + \frac{2}{a + 2} 
2/(2 + a) + (-2 + a)/((4 + a^2 + 4*a)*(-2/(a^2 + 2*a) + a/(-4 + 2*a) + (4 + a^2)/(8 - 2*a)))
Combinatoria [src] 
    /      5             2      4       3\  
  2*\32 + a  - 24*a - 8*a  - 2*a  + 10*a /  
--------------------------------------------
        /      5    4             3       2\
(2 + a)*\32 + a  - a  - 40*a + 2*a  + 12*a /
2(a5−2a4+10a3−8a2−24a+32)(a+2)(a5−a4+2a3+12a2−40a+32)\frac{2 \left(a^{5} - 2 a^{4} + 10 a^{3} - 8 a^{2} - 24 a + 32\right)}{\left(a + 2\right) \left(a^{5} - a^{4} + 2 a^{3} + 12 a^{2} - 40 a + 32\right)} 
2*(32 + a^5 - 24*a - 8*a^2 - 2*a^4 + 10*a^3)/((2 + a)*(32 + a^5 - a^4 - 40*a + 2*a^3 + 12*a^2))
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