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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
       ___          x   ___   ___       
     \/ 3          3 *\/ 3 *\/ x *log(3)
---------------- - ---------------------
    ___ / x    \                 2      
2*\/ x *\3  + 1/         / x    \       
                         \3  + 1/
$$- \frac{\sqrt{x} \sqrt{3} \cdot 3^{x} \log{\left(3 \right)}}{\left(3^{x} + 1\right)^{2}} + \frac{\sqrt{3}}{2 \sqrt{x} \left(3^{x} + 1\right)}$$ 
sqrt(3)/(((2*sqrt(x))*(3^x + 1))) - ((3^x*sqrt(3))*sqrt(x))*log(3)/(3^x + 1)^2
Simplificación general [src] 
  ___ /     x\      1/2 + x       
\/ 3 *\1 + 3 / - x*3       *log(9)
----------------------------------
                        2         
            ___ /     x\          
        2*\/ x *\1 + 3 /
$$\frac{- 3^{x + \frac{1}{2}} x \log{\left(9 \right)} + \sqrt{3} \left(3^{x} + 1\right)}{2 \sqrt{x} \left(3^{x} + 1\right)^{2}}$$ 
(sqrt(3)*(1 + 3^x) - x*3^(1/2 + x)*log(9))/(2*sqrt(x)*(1 + 3^x)^2)
Respuesta numérica [src] 
0.866025403784439*x^(-0.5)/(1.0 + 3.0^x) - 1.90285230179269*3.0^x*x^0.5/(1.0 + 3.0^x)^2
0.866025403784439*x^(-0.5)/(1.0 + 3.0^x) - 1.90285230179269*3.0^x*x^0.5/(1.0 + 3.0^x)^2
Denominador racional [src] 
                    2                                                    
  ___   ___ /     x\        ___  x  3/2              ___  2*x  3/2       
\/ 3 *\/ x *\1 + 3 /  - 2*\/ 3 *3 *x   *log(3) - 2*\/ 3 *3   *x   *log(3)
-------------------------------------------------------------------------
                                          3                              
                                  /     x\                               
                              2*x*\1 + 3 /
$$\frac{- 2 \sqrt{3} \cdot 3^{2 x} x^{\frac{3}{2}} \log{\left(3 \right)} - 2 \sqrt{3} \cdot 3^{x} x^{\frac{3}{2}} \log{\left(3 \right)} + \sqrt{3} \sqrt{x} \left(3^{x} + 1\right)^{2}}{2 x \left(3^{x} + 1\right)^{3}}$$ 
(sqrt(3)*sqrt(x)*(1 + 3^x)^2 - 2*sqrt(3)*3^x*x^(3/2)*log(3) - 2*sqrt(3)*3^(2*x)*x^(3/2)*log(3))/(2*x*(1 + 3^x)^3)
Potencias [src] 
       ___           ___  x   ___       
     \/ 3          \/ 3 *3 *\/ x *log(3)
---------------- - ---------------------
  ___ /       x\                 2      
\/ x *\2 + 2*3 /         /     x\       
                         \1 + 3 /
$$- \frac{\sqrt{3} \cdot 3^{x} \sqrt{x} \log{\left(3 \right)}}{\left(3^{x} + 1\right)^{2}} + \frac{\sqrt{3}}{\sqrt{x} \left(2 \cdot 3^{x} + 2\right)}$$ 
       ___          1/2 + x   ___       
     \/ 3          3       *\/ x *log(3)
---------------- - ---------------------
  ___ /       x\                 2      
\/ x *\2 + 2*3 /         /     x\       
                         \1 + 3 /
$$- \frac{3^{x + \frac{1}{2}} \sqrt{x} \log{\left(3 \right)}}{\left(3^{x} + 1\right)^{2}} + \frac{\sqrt{3}}{\sqrt{x} \left(2 \cdot 3^{x} + 2\right)}$$ 
       ___          1/2 + x   ___       
     \/ 3          3       *\/ x *log(3)
---------------- - ---------------------
    ___ /     x\                 2      
2*\/ x *\1 + 3 /         /     x\       
                         \1 + 3 /
$$- \frac{3^{x + \frac{1}{2}} \sqrt{x} \log{\left(3 \right)}}{\left(3^{x} + 1\right)^{2}} + \frac{\sqrt{3}}{2 \sqrt{x} \left(3^{x} + 1\right)}$$ 
sqrt(3)/(2*sqrt(x)*(1 + 3^x)) - 3^(1/2 + x)*sqrt(x)*log(3)/(1 + 3^x)^2
Combinatoria [src] 
   ___ /      x        x       \ 
-\/ 3 *\-1 - 3  + 2*x*3 *log(3)/ 
---------------------------------
                        2        
            ___ /     x\         
        2*\/ x *\1 + 3 /
$$- \frac{\sqrt{3} \left(2 \cdot 3^{x} x \log{\left(3 \right)} - 3^{x} - 1\right)}{2 \sqrt{x} \left(3^{x} + 1\right)^{2}}$$ 
-sqrt(3)*(-1 - 3^x + 2*x*3^x*log(3))/(2*sqrt(x)*(1 + 3^x)^2)
Parte trigonométrica [src] 
       ___           ___  x   ___       
     \/ 3          \/ 3 *3 *\/ x *log(3)
---------------- - ---------------------
    ___ /     x\                 2      
2*\/ x *\1 + 3 /         /     x\       
                         \1 + 3 /
$$- \frac{\sqrt{3} \cdot 3^{x} \sqrt{x} \log{\left(3 \right)}}{\left(3^{x} + 1\right)^{2}} + \frac{\sqrt{3}}{2 \sqrt{x} \left(3^{x} + 1\right)}$$ 
sqrt(3)/(2*sqrt(x)*(1 + 3^x)) - sqrt(3)*3^x*sqrt(x)*log(3)/(1 + 3^x)^2
Unión de expresiones racionales [src] 
  ___ /     x        x       \
\/ 3 *\1 + 3  - 2*x*3 *log(3)/
------------------------------
                      2       
          ___ /     x\        
      2*\/ x *\1 + 3 /
$$\frac{\sqrt{3} \left(- 2 \cdot 3^{x} x \log{\left(3 \right)} + 3^{x} + 1\right)}{2 \sqrt{x} \left(3^{x} + 1\right)^{2}}$$ 
sqrt(3)*(1 + 3^x - 2*x*3^x*log(3))/(2*sqrt(x)*(1 + 3^x)^2)
Denominador común [src] 
 /    ___     ___  x         ___  x       \ 
-\- \/ 3  - \/ 3 *3  + 2*x*\/ 3 *3 *log(3)/ 
--------------------------------------------
        ___      2*x   ___      x   ___     
    2*\/ x  + 2*3   *\/ x  + 4*3 *\/ x
$$- \frac{2 \sqrt{3} \cdot 3^{x} x \log{\left(3 \right)} - \sqrt{3} \cdot 3^{x} - \sqrt{3}}{2 \cdot 3^{2 x} \sqrt{x} + 4 \cdot 3^{x} \sqrt{x} + 2 \sqrt{x}}$$ 
-(-sqrt(3) - sqrt(3)*3^x + 2*x*sqrt(3)*3^x*log(3))/(2*sqrt(x) + 2*3^(2*x)*sqrt(x) + 4*3^x*sqrt(x))
Compilar la expresión [src] 
       ___           ___  x   ___       
     \/ 3          \/ 3 *3 *\/ x *log(3)
---------------- - ---------------------
    ___ /     x\                 2      
2*\/ x *\1 + 3 /         /     x\       
                         \1 + 3 /
$$- \frac{\sqrt{3} \cdot 3^{x} \sqrt{x} \log{\left(3 \right)}}{\left(3^{x} + 1\right)^{2}} + \frac{\sqrt{3}}{2 \sqrt{x} \left(3^{x} + 1\right)}$$ 
sqrt(3)/(2*sqrt(x)*(1 + 3^x)) - sqrt(3)*3^x*sqrt(x)*log(3)/(1 + 3^x)^2
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