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Simplificación de expresiones/ Descomposición en fracciones simples/ 8*(-1+4*(1+x)^2/(-3+x^2+2*x))/(-3+x^2+2*x)^2

¿Cómo vas a descomponer esta 8*(-1+4*(1+x)^2/(-3+x^2+2*x))/(-3+x^2+2*x)^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  /                2 \
  |       4*(1 + x)  |
8*|-1 + -------------|
  |           2      |
  \     -3 + x  + 2*x/
----------------------
                  2   
   /      2      \    
   \-3 + x  + 2*x/
$$\frac{8 \left(\frac{4 \left(x + 1\right)^{2}}{2 x + \left(x^{2} - 3\right)} - 1\right)}{\left(2 x + \left(x^{2} - 3\right)\right)^{2}}$$ 
(8*(-1 + (4*(1 + x)^2)/(-3 + x^2 + 2*x)))/(-3 + x^2 + 2*x)^2
Simplificación general [src] 
  /     2                  2\
8*\3 - x  - 2*x + 4*(1 + x) /
-----------------------------
                      3      
       /      2      \       
       \-3 + x  + 2*x/
$$\frac{8 \left(- x^{2} - 2 x + 4 \left(x + 1\right)^{2} + 3\right)}{\left(x^{2} + 2 x - 3\right)^{3}}$$ 
8*(3 - x^2 - 2*x + 4*(1 + x)^2)/(-3 + x^2 + 2*x)^3
Descomposición de una fracción [src] 
-2/(3 + x)^3 + 2/(-1 + x)^3
$$- \frac{2}{\left(x + 3\right)^{3}} + \frac{2}{\left(x - 1\right)^{3}}$$ 
     2           2    
- -------- + ---------
         3           3
  (3 + x)    (-1 + x)
Respuesta numérica [src] 
0.111111111111111*(-8.0 + 32.0*(1.0 + x)^2/(-3.0 + x^2 + 2.0*x))/(-1 + 0.333333333333333*x^2 + 0.666666666666667*x)^2
0.111111111111111*(-8.0 + 32.0*(1.0 + x)^2/(-3.0 + x^2 + 2.0*x))/(-1 + 0.333333333333333*x^2 + 0.666666666666667*x)^2
Compilar la expresión [src] 
                2 
      32*(1 + x)  
-8 + -------------
           2      
     -3 + x  + 2*x
------------------
                2 
 /      2      \  
 \-3 + x  + 2*x/
$$\frac{\frac{32 \left(x + 1\right)^{2}}{x^{2} + 2 x - 3} - 8}{\left(x^{2} + 2 x - 3\right)^{2}}$$ 
(-8 + 32*(1 + x)^2/(-3 + x^2 + 2*x))/(-3 + x^2 + 2*x)^2
Potencias [src] 
                2 
      32*(1 + x)  
-8 + -------------
           2      
     -3 + x  + 2*x
------------------
                2 
 /      2      \  
 \-3 + x  + 2*x/
$$\frac{\frac{32 \left(x + 1\right)^{2}}{x^{2} + 2 x - 3} - 8}{\left(x^{2} + 2 x - 3\right)^{2}}$$ 
(-8 + 32*(1 + x)^2/(-3 + x^2 + 2*x))/(-3 + x^2 + 2*x)^2
Combinatoria [src] 
  /       2      \
8*\7 + 3*x  + 6*x/
------------------
        3        3
(-1 + x) *(3 + x)
$$\frac{8 \left(3 x^{2} + 6 x + 7\right)}{\left(x - 1\right)^{3} \left(x + 3\right)^{3}}$$ 
8*(7 + 3*x^2 + 6*x)/((-1 + x)^3*(3 + x)^3)
Denominador racional [src] 
               2             2
24 - 16*x - 8*x  + 32*(1 + x) 
------------------------------
                      3       
       /      2      \        
       \-3 + x  + 2*x/
$$\frac{- 8 x^{2} - 16 x + 32 \left(x + 1\right)^{2} + 24}{\left(x^{2} + 2 x - 3\right)^{3}}$$ 
(24 - 16*x - 8*x^2 + 32*(1 + x)^2)/(-3 + x^2 + 2*x)^3
Parte trigonométrica [src] 
                2 
      32*(1 + x)  
-8 + -------------
           2      
     -3 + x  + 2*x
------------------
                2 
 /      2      \  
 \-3 + x  + 2*x/
$$\frac{\frac{32 \left(x + 1\right)^{2}}{x^{2} + 2 x - 3} - 8}{\left(x^{2} + 2 x - 3\right)^{2}}$$ 
(-8 + 32*(1 + x)^2/(-3 + x^2 + 2*x))/(-3 + x^2 + 2*x)^2
Unión de expresiones racionales [src] 
  /     2                  2\
8*\3 - x  - 2*x + 4*(1 + x) /
-----------------------------
                      3      
       /      2      \       
       \-3 + x  + 2*x/
$$\frac{8 \left(- x^{2} - 2 x + 4 \left(x + 1\right)^{2} + 3\right)}{\left(x^{2} + 2 x - 3\right)^{3}}$$ 
8*(3 - x^2 - 2*x + 4*(1 + x)^2)/(-3 + x^2 + 2*x)^3
Denominador común [src] 
                      2                     
             56 + 24*x  + 48*x              
--------------------------------------------
       6       3      2      4      5       
-27 + x  - 28*x  - 9*x  + 3*x  + 6*x  + 54*x
$$\frac{24 x^{2} + 48 x + 56}{x^{6} + 6 x^{5} + 3 x^{4} - 28 x^{3} - 9 x^{2} + 54 x - 27}$$ 
(56 + 24*x^2 + 48*x)/(-27 + x^6 - 28*x^3 - 9*x^2 + 3*x^4 + 6*x^5 + 54*x)
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