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

Expresión a simplificar:

Solución

Ha introducido [src]
   1      log(x)
------- - ------
    ___      3/2
x*\/ x    2*x   
$$\frac{1}{\sqrt{x} x} - \frac{\log{\left(x \right)}}{2 x^{\frac{3}{2}}}$$
1/(x*sqrt(x)) - log(x)/(2*x^(3/2))
Simplificación general [src]
2 - log(x)
----------
     3/2  
  2*x     
$$\frac{2 - \log{\left(x \right)}}{2 x^{\frac{3}{2}}}$$
(2 - log(x))/(2*x^(3/2))
Potencias [src]
 1     log(x)
---- - ------
 3/2      3/2
x      2*x   
$$- \frac{\log{\left(x \right)}}{2 x^{\frac{3}{2}}} + \frac{1}{x^{\frac{3}{2}}}$$
x^(-3/2) - log(x)/(2*x^(3/2))
Respuesta numérica [src]
x^(-1.5) - 0.5*x^(-1.5)*log(x)
x^(-1.5) - 0.5*x^(-1.5)*log(x)
Denominador común [src]
-(-2 + log(x)) 
---------------
        3/2    
     2*x       
$$- \frac{\log{\left(x \right)} - 2}{2 x^{\frac{3}{2}}}$$
-(-2 + log(x))/(2*x^(3/2))
Compilar la expresión [src]
 1     log(x)
---- - ------
 3/2      3/2
x      2*x   
$$- \frac{\log{\left(x \right)}}{2 x^{\frac{3}{2}}} + \frac{1}{x^{\frac{3}{2}}}$$
x^(-3/2) - log(x)/(2*x^(3/2))
Parte trigonométrica [src]
 1     log(x)
---- - ------
 3/2      3/2
x      2*x   
$$- \frac{\log{\left(x \right)}}{2 x^{\frac{3}{2}}} + \frac{1}{x^{\frac{3}{2}}}$$
x^(-3/2) - log(x)/(2*x^(3/2))
Unión de expresiones racionales [src]
2 - log(x)
----------
     3/2  
  2*x     
$$\frac{2 - \log{\left(x \right)}}{2 x^{\frac{3}{2}}}$$
(2 - log(x))/(2*x^(3/2))
Combinatoria [src]
-(-2 + log(x)) 
---------------
        3/2    
     2*x       
$$- \frac{\log{\left(x \right)} - 2}{2 x^{\frac{3}{2}}}$$
-(-2 + log(x))/(2*x^(3/2))
Denominador racional [src]
   3/2    3/2       
2*x    - x   *log(x)
--------------------
           3        
        2*x         
$$\frac{- x^{\frac{3}{2}} \log{\left(x \right)} + 2 x^{\frac{3}{2}}}{2 x^{3}}$$
(2*x^(3/2) - x^(3/2)*log(x))/(2*x^3)