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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
atan(x)    x - 3  
------- + --------
   2             2
          2 + 2*x
x−32x2+2+atan⁡(x)2\frac{x - 3}{2 x^{2} + 2} + \frac{\operatorname{atan}{\left(x \right)}}{2} 
atan(x)/2 + (x - 3)/(2 + 2*x^2)
Simplificación general [src] 
         /     2\        
-3 + x + \1 + x /*atan(x)
-------------------------
          /     2\       
        2*\1 + x /
x+(x2+1)atan⁡(x)−32(x2+1)\frac{x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)} - 3}{2 \left(x^{2} + 1\right)} 
(-3 + x + (1 + x^2)*atan(x))/(2*(1 + x^2))
Respuesta numérica [src] 
0.5*atan(x) + (-3.0 + x)/(2.0 + 2.0*x^2)
0.5*atan(x) + (-3.0 + x)/(2.0 + 2.0*x^2)
Unión de expresiones racionales [src] 
         /     2\        
-3 + x + \1 + x /*atan(x)
-------------------------
          /     2\       
        2*\1 + x /
x+(x2+1)atan⁡(x)−32(x2+1)\frac{x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)} - 3}{2 \left(x^{2} + 1\right)} 
(-3 + x + (1 + x^2)*atan(x))/(2*(1 + x^2))
Combinatoria [src] 
          2                  
-3 + x + x *atan(x) + atan(x)
-----------------------------
            /     2\         
          2*\1 + x /
x2atan⁡(x)+x+atan⁡(x)−32(x2+1)\frac{x^{2} \operatorname{atan}{\left(x \right)} + x + \operatorname{atan}{\left(x \right)} - 3}{2 \left(x^{2} + 1\right)} 
(-3 + x + x^2*atan(x) + atan(x))/(2*(1 + x^2))
Denominador racional [src] 
           /       2\        
-6 + 2*x + \2 + 2*x /*atan(x)
-----------------------------
                  2          
           4 + 4*x
2x+(2x2+2)atan⁡(x)−64x2+4\frac{2 x + \left(2 x^{2} + 2\right) \operatorname{atan}{\left(x \right)} - 6}{4 x^{2} + 4} 
(-6 + 2*x + (2 + 2*x^2)*atan(x))/(4 + 4*x^2)
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