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

Expresión a simplificar:

Solución

Ha introducido [src]
atan(x)       x     
------- - ----------
   2        /     2\
          2*\1 + x /
$$- \frac{x}{2 \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
atan(x)/2 - x/(2*(1 + x^2))
Simplificación general [src]
     /     2\        
-x + \1 + x /*atan(x)
---------------------
        /     2\     
      2*\1 + x /     
$$\frac{- x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{2 \left(x^{2} + 1\right)}$$
(-x + (1 + x^2)*atan(x))/(2*(1 + x^2))
Respuesta numérica [src]
0.5*atan(x) - x/(2.0 + 2.0*x^2)
0.5*atan(x) - x/(2.0 + 2.0*x^2)
Compilar la expresión [src]
atan(x)      x    
------- - --------
   2             2
          2 + 2*x 
$$- \frac{x}{2 x^{2} + 2} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
atan(x)/2 - x/(2 + 2*x^2)
Denominador racional [src]
       /       2\        
-2*x + \2 + 2*x /*atan(x)
-------------------------
                2        
         4 + 4*x         
$$\frac{- 2 x + \left(2 x^{2} + 2\right) \operatorname{atan}{\left(x \right)}}{4 x^{2} + 4}$$
(-2*x + (2 + 2*x^2)*atan(x))/(4 + 4*x^2)
Parte trigonométrica [src]
atan(x)      x    
------- - --------
   2             2
          2 + 2*x 
$$- \frac{x}{2 x^{2} + 2} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
atan(x)/2 - x/(2 + 2*x^2)
Potencias [src]
atan(x)      x    
------- - --------
   2             2
          2 + 2*x 
$$- \frac{x}{2 x^{2} + 2} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
atan(x)/2 - x/(2 + 2*x^2)
Denominador común [src]
atan(x)      x    
------- - --------
   2             2
          2 + 2*x 
$$- \frac{x}{2 x^{2} + 2} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
atan(x)/2 - x/(2 + 2*x^2)
Unión de expresiones racionales [src]
     /     2\        
-x + \1 + x /*atan(x)
---------------------
        /     2\     
      2*\1 + x /     
$$\frac{- x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{2 \left(x^{2} + 1\right)}$$
(-x + (1 + x^2)*atan(x))/(2*(1 + x^2))
Combinatoria [src]
      2                  
-x + x *atan(x) + atan(x)
-------------------------
          /     2\       
        2*\1 + x /       
$$\frac{x^{2} \operatorname{atan}{\left(x \right)} - x + \operatorname{atan}{\left(x \right)}}{2 \left(x^{2} + 1\right)}$$
(-x + x^2*atan(x) + atan(x))/(2*(1 + x^2))