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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   /    1\            
log|E + -|            
   \    x/       1    
---------- - ---------
    2        2*E*x + 2
log⁡(e+1x)2−12ex+2\frac{\log{\left(e + \frac{1}{x} \right)}}{2} - \frac{1}{2 e x + 2} 
log(E + 1/x)/2 - 1/((2*E)*x + 2)
Simplificación general [src] 
                  /1 + E*x\
-1 + (1 + E*x)*log|-------|
                  \   x   /
---------------------------
        2*(1 + E*x)
(ex+1)log⁡(ex+1x)−12(ex+1)\frac{\left(e x + 1\right) \log{\left(\frac{e x + 1}{x} \right)} - 1}{2 \left(e x + 1\right)} 
(-1 + (1 + E*x)*log((1 + E*x)/x))/(2*(1 + E*x))
Respuesta numérica [src] 
-1/(2.0 + 5.43656365691809*x) + 0.5*log(E + 1/x)
-1/(2.0 + 5.43656365691809*x) + 0.5*log(E + 1/x)
Unión de expresiones racionales [src] 
                  /1 + E*x\
-1 + (1 + E*x)*log|-------|
                  \   x   /
---------------------------
        2*(1 + E*x)
(ex+1)log⁡(ex+1x)−12(ex+1)\frac{\left(e x + 1\right) \log{\left(\frac{e x + 1}{x} \right)} - 1}{2 \left(e x + 1\right)} 
(-1 + (1 + E*x)*log((1 + E*x)/x))/(2*(1 + E*x))
Combinatoria [src] 
            /    1\      /    1\
-1 + E*x*log|E + -| + log|E + -|
            \    x/      \    x/
--------------------------------
          2*(1 + E*x)
exlog⁡(e+1x)+log⁡(e+1x)−12(ex+1)\frac{e x \log{\left(e + \frac{1}{x} \right)} + \log{\left(e + \frac{1}{x} \right)} - 1}{2 \left(e x + 1\right)} 
(-1 + E*x*log(E + 1/x) + log(E + 1/x))/(2*(1 + E*x))
Denominador racional [src] 
                    /    1\
-2 + (2 + 2*E*x)*log|E + -|
                    \    x/
---------------------------
         4 + 4*E*x
(2ex+2)log⁡(e+1x)−24ex+4\frac{\left(2 e x + 2\right) \log{\left(e + \frac{1}{x} \right)} - 2}{4 e x + 4} 
(-2 + (2 + 2*E*x)*log(E + 1/x))/(4 + 4*E*x)
Parte trigonométrica [src] 
   /1                    \                                
log|- + cosh(1) + sinh(1)|                                
   \x                    /                 1              
-------------------------- - -----------------------------
            2                2 + x*(2*cosh(1) + 2*sinh(1))
log⁡(sinh⁡(1)+cosh⁡(1)+1x)2−1x(2sinh⁡(1)+2cosh⁡(1))+2\frac{\log{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)} + \frac{1}{x} \right)}}{2} - \frac{1}{x \left(2 \sinh{\left(1 \right)} + 2 \cosh{\left(1 \right)}\right) + 2} 
   /1                    \                              
log|- + cosh(1) + sinh(1)|                              
   \x                    /                1             
-------------------------- - ---------------------------
            2                2 + 2*x*(cosh(1) + sinh(1))
log⁡(sinh⁡(1)+cosh⁡(1)+1x)2−12x(sinh⁡(1)+cosh⁡(1))+2\frac{\log{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)} + \frac{1}{x} \right)}}{2} - \frac{1}{2 x \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right) + 2} 
log(1/x + cosh(1) + sinh(1))/2 - 1/(2 + 2*x*(cosh(1) + sinh(1)))
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