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Simplificación de expresiones/ Descomposición en fracciones simples/ atan(x/10)/5-x/(100+x^2)

¿Cómo vas a descomponer esta atan(x/10)/5-x/(100+x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /x \           
atan|--|           
    \10/      x    
-------- - --------
   5              2
           100 + x
−xx2+100+atan⁡(x10)5- \frac{x}{x^{2} + 100} + \frac{\operatorname{atan}{\left(\frac{x}{10} \right)}}{5} 
atan(x/10)/5 - x/(100 + x^2)
Simplificación general [src] 
     /       2\     /x \
     \100 + x /*atan|--|
                    \10/
-x + -------------------
              5         
------------------------
               2        
        100 + x
−x+(x2+100)atan⁡(x10)5x2+100\frac{- x + \frac{\left(x^{2} + 100\right) \operatorname{atan}{\left(\frac{x}{10} \right)}}{5}}{x^{2} + 100} 
(-x + (100 + x^2)*atan(x/10)/5)/(100 + x^2)
Denominador racional [src] 
       /       2\     /x \
-5*x + \100 + x /*atan|--|
                      \10/
--------------------------
                 2        
        500 + 5*x
−5x+(x2+100)atan⁡(x10)5x2+500\frac{- 5 x + \left(x^{2} + 100\right) \operatorname{atan}{\left(\frac{x}{10} \right)}}{5 x^{2} + 500} 
(-5*x + (100 + x^2)*atan(x/10))/(500 + 5*x^2)
Unión de expresiones racionales [src] 
       /       2\     /x \
-5*x + \100 + x /*atan|--|
                      \10/
--------------------------
         /       2\       
       5*\100 + x /
−5x+(x2+100)atan⁡(x10)5(x2+100)\frac{- 5 x + \left(x^{2} + 100\right) \operatorname{atan}{\left(\frac{x}{10} \right)}}{5 \left(x^{2} + 100\right)} 
(-5*x + (100 + x^2)*atan(x/10))/(5*(100 + x^2))
Combinatoria [src] 
               /x \    2     /x \
-5*x + 100*atan|--| + x *atan|--|
               \10/          \10/
---------------------------------
             /       2\          
           5*\100 + x /
x2atan⁡(x10)−5x+100atan⁡(x10)5(x2+100)\frac{x^{2} \operatorname{atan}{\left(\frac{x}{10} \right)} - 5 x + 100 \operatorname{atan}{\left(\frac{x}{10} \right)}}{5 \left(x^{2} + 100\right)} 
(-5*x + 100*atan(x/10) + x^2*atan(x/10))/(5*(100 + x^2))
Respuesta numérica [src] 
0.2*atan(x/10) - x/(100.0 + x^2)
0.2*atan(x/10) - x/(100.0 + x^2)
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