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¿Cómo vas a descomponer esta ((a^3-a^2-a-2)/(a^3+1))*((a^3-2*a^2+2*a-1)/(a^3+a^2+a))*((a^2+2)/(a^2-3*a+2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
 3    2          3      2               2       
a  - a  - a - 2 a  - 2*a  + 2*a - 1    a  + 2   
---------------*-------------------*------------
      3              3    2          2          
     a  + 1         a  + a  + a     a  - 3*a + 2
(2a+(a32a2))1a+(a3+a2)(a+(a3a2))2a3+1a2+2(a23a)+2\frac{\left(2 a + \left(a^{3} - 2 a^{2}\right)\right) - 1}{a + \left(a^{3} + a^{2}\right)} \frac{\left(- a + \left(a^{3} - a^{2}\right)\right) - 2}{a^{3} + 1} \frac{a^{2} + 2}{\left(a^{2} - 3 a\right) + 2}
(((a^3 - a^2 - a - 2)/(a^3 + 1))*((a^3 - 2*a^2 + 2*a - 1)/(a^3 + a^2 + a)))*((a^2 + 2)/(a^2 - 3*a + 2))
Simplificación general [src]
       2 
  2 + a  
---------
a*(1 + a)
a2+2a(a+1)\frac{a^{2} + 2}{a \left(a + 1\right)}
(2 + a^2)/(a*(1 + a))
Descomposición de una fracción [src]
1 - 3/(1 + a) + 2/a
13a+1+2a1 - \frac{3}{a + 1} + \frac{2}{a}
      3     2
1 - ----- + -
    1 + a   a
Parte trigonométrica [src]
/     2\ /      3      2      \ /      3        2\
\2 + a /*\-1 + a  - 2*a  + 2*a/*\-2 + a  - a - a /
--------------------------------------------------
      /     3\ /     2      \ /     2    3\       
      \1 + a /*\2 + a  - 3*a/*\a + a  + a /       
(a2+2)(a32a2+2a1)(a3a2a2)(a3+1)(a23a+2)(a3+a2+a)\frac{\left(a^{2} + 2\right) \left(a^{3} - 2 a^{2} + 2 a - 1\right) \left(a^{3} - a^{2} - a - 2\right)}{\left(a^{3} + 1\right) \left(a^{2} - 3 a + 2\right) \left(a^{3} + a^{2} + a\right)}
(2 + a^2)*(-1 + a^3 - 2*a^2 + 2*a)*(-2 + a^3 - a - a^2)/((1 + a^3)*(2 + a^2 - 3*a)*(a + a^2 + a^3))
Denominador común [src]
    -2 + a
1 - ------
         2
    a + a 
a2a2+a+1- \frac{a - 2}{a^{2} + a} + 1
1 - (-2 + a)/(a + a^2)
Unión de expresiones racionales [src]
                                                     /     2\
(-1 + a*(2 + a*(-2 + a)))*(-2 + a*(-1 + a*(-1 + a)))*\2 + a /
-------------------------------------------------------------
           /     3\                                          
         a*\1 + a /*(1 + a*(1 + a))*(2 + a*(-3 + a))         
(a2+2)(a(a(a2)+2)1)(a(a(a1)1)2)a(a3+1)(a(a3)+2)(a(a+1)+1)\frac{\left(a^{2} + 2\right) \left(a \left(a \left(a - 2\right) + 2\right) - 1\right) \left(a \left(a \left(a - 1\right) - 1\right) - 2\right)}{a \left(a^{3} + 1\right) \left(a \left(a - 3\right) + 2\right) \left(a \left(a + 1\right) + 1\right)}
(-1 + a*(2 + a*(-2 + a)))*(-2 + a*(-1 + a*(-1 + a)))*(2 + a^2)/(a*(1 + a^3)*(1 + a*(1 + a))*(2 + a*(-3 + a)))
Combinatoria [src]
       2 
  2 + a  
---------
a*(1 + a)
a2+2a(a+1)\frac{a^{2} + 2}{a \left(a + 1\right)}
(2 + a^2)/(a*(1 + a))
Respuesta numérica [src]
(2.0 + a^2)*(-1.0 + a^3 + 2.0*a - 2.0*a^2)*(-2.0 + a^3 - a - a^2)/((1.0 + a^3)*(2.0 + a^2 - 3.0*a)*(a + a^2 + a^3))
(2.0 + a^2)*(-1.0 + a^3 + 2.0*a - 2.0*a^2)*(-2.0 + a^3 - a - a^2)/((1.0 + a^3)*(2.0 + a^2 - 3.0*a)*(a + a^2 + a^3))
Denominador racional [src]
/     2\ /      3      2      \ /      3        2\
\2 + a /*\-1 + a  - 2*a  + 2*a/*\-2 + a  - a - a /
--------------------------------------------------
      /     3\ /     2      \ /     2    3\       
      \1 + a /*\2 + a  - 3*a/*\a + a  + a /       
(a2+2)(a32a2+2a1)(a3a2a2)(a3+1)(a23a+2)(a3+a2+a)\frac{\left(a^{2} + 2\right) \left(a^{3} - 2 a^{2} + 2 a - 1\right) \left(a^{3} - a^{2} - a - 2\right)}{\left(a^{3} + 1\right) \left(a^{2} - 3 a + 2\right) \left(a^{3} + a^{2} + a\right)}
(2 + a^2)*(-1 + a^3 - 2*a^2 + 2*a)*(-2 + a^3 - a - a^2)/((1 + a^3)*(2 + a^2 - 3*a)*(a + a^2 + a^3))
Potencias [src]
/     2\ /      3      2      \ /      3        2\
\2 + a /*\-1 + a  - 2*a  + 2*a/*\-2 + a  - a - a /
--------------------------------------------------
      /     3\ /     2      \ /     2    3\       
      \1 + a /*\2 + a  - 3*a/*\a + a  + a /       
(a2+2)(a32a2+2a1)(a3a2a2)(a3+1)(a23a+2)(a3+a2+a)\frac{\left(a^{2} + 2\right) \left(a^{3} - 2 a^{2} + 2 a - 1\right) \left(a^{3} - a^{2} - a - 2\right)}{\left(a^{3} + 1\right) \left(a^{2} - 3 a + 2\right) \left(a^{3} + a^{2} + a\right)}
(2 + a^2)*(-1 + a^3 - 2*a^2 + 2*a)*(-2 + a^3 - a - a^2)/((1 + a^3)*(2 + a^2 - 3*a)*(a + a^2 + a^3))
Compilar la expresión [src]
/     2\ /      3      2      \ /      3        2\
\2 + a /*\-1 + a  - 2*a  + 2*a/*\-2 + a  - a - a /
--------------------------------------------------
      /     3\ /     2      \ /     2    3\       
      \1 + a /*\2 + a  - 3*a/*\a + a  + a /       
(a2+2)(a32a2+2a1)(a3a2a2)(a3+1)(a23a+2)(a3+a2+a)\frac{\left(a^{2} + 2\right) \left(a^{3} - 2 a^{2} + 2 a - 1\right) \left(a^{3} - a^{2} - a - 2\right)}{\left(a^{3} + 1\right) \left(a^{2} - 3 a + 2\right) \left(a^{3} + a^{2} + a\right)}
(2 + a^2)*(-1 + a^3 - 2*a^2 + 2*a)*(-2 + a^3 - a - a^2)/((1 + a^3)*(2 + a^2 - 3*a)*(a + a^2 + a^3))