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

Expresión a simplificar:

Solución

Ha introducido [src]
         1    1  
log(x) - - - ----
         x      2
             2*x 
(log(x)1x)12x2\left(\log{\left(x \right)} - \frac{1}{x}\right) - \frac{1}{2 x^{2}}
log(x) - 1/x - 1/(2*x^2)
Simplificación general [src]
  1    1           
- - - ---- + log(x)
  x      2         
      2*x          
log(x)1x12x2\log{\left(x \right)} - \frac{1}{x} - \frac{1}{2 x^{2}}
-1/x - 1/(2*x^2) + log(x)
Denominador común [src]
  1 + 2*x         
- ------- + log(x)
       2          
    2*x           
log(x)2x+12x2\log{\left(x \right)} - \frac{2 x + 1}{2 x^{2}}
-(1 + 2*x)/(2*x^2) + log(x)
Denominador racional [src]
        2                
-x + 2*x *(-1 + x*log(x))
-------------------------
              3          
           2*x           
2x2(xlog(x)1)x2x3\frac{2 x^{2} \left(x \log{\left(x \right)} - 1\right) - x}{2 x^{3}}
(-x + 2*x^2*(-1 + x*log(x)))/(2*x^3)
Potencias [src]
  1    1           
- - - ---- + log(x)
  x      2         
      2*x          
log(x)1x12x2\log{\left(x \right)} - \frac{1}{x} - \frac{1}{2 x^{2}}
-1/x - 1/(2*x^2) + log(x)
Unión de expresiones racionales [src]
-1 + 2*x*(-1 + x*log(x))
------------------------
             2          
          2*x           
2x(xlog(x)1)12x2\frac{2 x \left(x \log{\left(x \right)} - 1\right) - 1}{2 x^{2}}
(-1 + 2*x*(-1 + x*log(x)))/(2*x^2)
Respuesta numérica [src]
-1/x - 0.5/x^2 + log(x)
-1/x - 0.5/x^2 + log(x)
Abrimos la expresión [src]
  1    1           
- - - ---- + log(x)
  x      2         
      2*x          
log(x)1x12x2\log{\left(x \right)} - \frac{1}{x} - \frac{1}{2 x^{2}}
-1/x - 1/(2*x^2) + log(x)
Compilar la expresión [src]
  1    1           
- - - ---- + log(x)
  x      2         
      2*x          
log(x)1x12x2\log{\left(x \right)} - \frac{1}{x} - \frac{1}{2 x^{2}}
-1/x - 1/(2*x^2) + log(x)
Parte trigonométrica [src]
  1    1           
- - - ---- + log(x)
  x      2         
      2*x          
log(x)1x12x2\log{\left(x \right)} - \frac{1}{x} - \frac{1}{2 x^{2}}
-1/x - 1/(2*x^2) + log(x)
Combinatoria [src]
              2       
-1 - 2*x + 2*x *log(x)
----------------------
            2         
         2*x          
2x2log(x)2x12x2\frac{2 x^{2} \log{\left(x \right)} - 2 x - 1}{2 x^{2}}
(-1 - 2*x + 2*x^2*log(x))/(2*x^2)