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Simplificación de expresiones/ Descomposición en fracciones simples/ ((x^3+3*x)/(x+2))-((3*x^2-14*x+16)/(x^2-4))-2*x

¿Cómo vas a descomponer esta ((x^3+3*x)/(x+2))-((3*x^2-14*x+16)/(x^2-4))-2*x expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
 3            2                  
x  + 3*x   3*x  - 14*x + 16      
-------- - ---------------- - 2*x
 x + 2           2               
                x  - 4
$$- 2 x + \left(- \frac{\left(3 x^{2} - 14 x\right) + 16}{x^{2} - 4} + \frac{x^{3} + 3 x}{x + 2}\right)$$ 
(x^3 + 3*x)/(x + 2) - (3*x^2 - 14*x + 16)/(x^2 - 4) - 2*x
Descomposición de una fracción [src] 
4 + x^2 - 4*x
$$x^{2} - 4 x + 4$$ 
     2      
4 + x  - 4*x
Simplificación general [src] 
     2      
4 + x  - 4*x
$$x^{2} - 4 x + 4$$ 
4 + x^2 - 4*x
Respuesta numérica [src] 
-2.0*x + (x^3 + 3.0*x)/(2.0 + x) - (16.0 + 3.0*x^2 - 14.0*x)/(-4.0 + x^2)
-2.0*x + (x^3 + 3.0*x)/(2.0 + x) - (16.0 + 3.0*x^2 - 14.0*x)/(-4.0 + x^2)
Denominador común [src] 
     2      
4 + x  - 4*x
$$x^{2} - 4 x + 4$$ 
4 + x^2 - 4*x
Denominador racional [src] 
/      2\ / 3      \           /         2       \       /      2\        
\-4 + x /*\x  + 3*x/ + (2 + x)*\-16 - 3*x  + 14*x/ - 2*x*\-4 + x /*(2 + x)
--------------------------------------------------------------------------
                            /      2\                                     
                            \-4 + x /*(2 + x)
$$\frac{- 2 x \left(x + 2\right) \left(x^{2} - 4\right) + \left(x + 2\right) \left(- 3 x^{2} + 14 x - 16\right) + \left(x^{2} - 4\right) \left(x^{3} + 3 x\right)}{\left(x + 2\right) \left(x^{2} - 4\right)}$$ 
((-4 + x^2)*(x^3 + 3*x) + (2 + x)*(-16 - 3*x^2 + 14*x) - 2*x*(-4 + x^2)*(2 + x))/((-4 + x^2)*(2 + x))
Combinatoria [src] 
        2
(-2 + x)
$$\left(x - 2\right)^{2}$$ 
(-2 + x)^2
Parte trigonométrica [src] 
        3                        2
       x  + 3*x   16 - 14*x + 3*x 
-2*x + -------- - ----------------
        2 + x               2     
                      -4 + x
$$- 2 x - \frac{3 x^{2} - 14 x + 16}{x^{2} - 4} + \frac{x^{3} + 3 x}{x + 2}$$ 
-2*x + (x^3 + 3*x)/(2 + x) - (16 - 14*x + 3*x^2)/(-4 + x^2)
Potencias [src] 
                2           3      
       -16 - 3*x  + 14*x   x  + 3*x
-2*x + ----------------- + --------
                  2         2 + x  
            -4 + x
$$- 2 x + \frac{- 3 x^{2} + 14 x - 16}{x^{2} - 4} + \frac{x^{3} + 3 x}{x + 2}$$ 
        3                        2
       x  + 3*x   16 - 14*x + 3*x 
-2*x + -------- - ----------------
        2 + x               2     
                      -4 + x
$$- 2 x - \frac{3 x^{2} - 14 x + 16}{x^{2} - 4} + \frac{x^{3} + 3 x}{x + 2}$$ 
-2*x + (x^3 + 3*x)/(2 + x) - (16 - 14*x + 3*x^2)/(-4 + x^2)
Unión de expresiones racionales [src] 
                                  /      2\ /     2\       /      2\        
-(2 + x)*(16 + x*(-14 + 3*x)) + x*\-4 + x /*\3 + x / - 2*x*\-4 + x /*(2 + x)
----------------------------------------------------------------------------
                             /      2\                                      
                             \-4 + x /*(2 + x)
$$\frac{- 2 x \left(x + 2\right) \left(x^{2} - 4\right) + x \left(x^{2} - 4\right) \left(x^{2} + 3\right) - \left(x + 2\right) \left(x \left(3 x - 14\right) + 16\right)}{\left(x + 2\right) \left(x^{2} - 4\right)}$$ 
(-(2 + x)*(16 + x*(-14 + 3*x)) + x*(-4 + x^2)*(3 + x^2) - 2*x*(-4 + x^2)*(2 + x))/((-4 + x^2)*(2 + x))
Compilar la expresión [src] 
        3                        2
       x  + 3*x   16 - 14*x + 3*x 
-2*x + -------- - ----------------
        2 + x               2     
                      -4 + x
$$- 2 x - \frac{3 x^{2} - 14 x + 16}{x^{2} - 4} + \frac{x^{3} + 3 x}{x + 2}$$ 
-2*x + (x^3 + 3*x)/(2 + x) - (16 - 14*x + 3*x^2)/(-4 + x^2)
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