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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(x)*(5/x+3*sqrt(x)/2)+(5*log(x)+x^(3/2))/(2*sqrt(x))

¿Cómo vas a descomponer esta sqrt(x)*(5/x+3*sqrt(x)/2)+(5*log(x)+x^(3/2))/(2*sqrt(x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
      /        ___\               3/2
  ___ |5   3*\/ x |   5*log(x) + x   
\/ x *|- + -------| + ---------------
      \x      2   /           ___    
                          2*\/ x
x(3x2+5x)+x32+5log⁡(x)2x\sqrt{x} \left(\frac{3 \sqrt{x}}{2} + \frac{5}{x}\right) + \frac{x^{\frac{3}{2}} + 5 \log{\left(x \right)}}{2 \sqrt{x}} 
sqrt(x)*(5/x + (3*sqrt(x))/2) + (5*log(x) + x^(3/2))/((2*sqrt(x)))
Simplificación general [src] 
        3/2           
10 + 4*x    + 5*log(x)
----------------------
           ___        
       2*\/ x
4x32+5log⁡(x)+102x\frac{4 x^{\frac{3}{2}} + 5 \log{\left(x \right)} + 10}{2 \sqrt{x}} 
(10 + 4*x^(3/2) + 5*log(x))/(2*sqrt(x))
Respuesta numérica [src] 
x^0.5*(1.5*x^0.5 + 5.0/x) + 0.5*x^(-0.5)*(x^1.5 + 5.0*log(x))
x^0.5*(1.5*x^0.5 + 5.0/x) + 0.5*x^(-0.5)*(x^1.5 + 5.0*log(x))
Combinatoria [src] 
        3/2           
10 + 4*x    + 5*log(x)
----------------------
           ___        
       2*\/ x
4x32+5log⁡(x)+102x\frac{4 x^{\frac{3}{2}} + 5 \log{\left(x \right)} + 10}{2 \sqrt{x}} 
(10 + 4*x^(3/2) + 5*log(x))/(2*sqrt(x))
Unión de expresiones racionales [src] 
        3/2           
10 + 4*x    + 5*log(x)
----------------------
           ___        
       2*\/ x
4x32+5log⁡(x)+102x\frac{4 x^{\frac{3}{2}} + 5 \log{\left(x \right)} + 10}{2 \sqrt{x}} 
(10 + 4*x^(3/2) + 5*log(x))/(2*sqrt(x))
Potencias [src] 
                       3/2           
                      x      5*log(x)
      /        ___\   ---- + --------
  ___ |5   3*\/ x |    2        2    
\/ x *|- + -------| + ---------------
      \x      2   /          ___     
                           \/ x
x(3x2+5x)+x322+5log⁡(x)2x\sqrt{x} \left(\frac{3 \sqrt{x}}{2} + \frac{5}{x}\right) + \frac{\frac{x^{\frac{3}{2}}}{2} + \frac{5 \log{\left(x \right)}}{2}}{\sqrt{x}} 
sqrt(x)*(5/x + 3*sqrt(x)/2) + (x^(3/2)/2 + 5*log(x)/2)/sqrt(x)
Denominador racional [src] 
          ____           ____           ____       
   5/2   /  3           /  3           /  3        
8*x   *\/  x   + 20*x*\/  x   + 10*x*\/  x  *log(x)
---------------------------------------------------
                           3                       
                        4*x
8x52x3+10xx3log⁡(x)+20xx34x3\frac{8 x^{\frac{5}{2}} \sqrt{x^{3}} + 10 x \sqrt{x^{3}} \log{\left(x \right)} + 20 x \sqrt{x^{3}}}{4 x^{3}} 
(8*x^(5/2)*sqrt(x^3) + 20*x*sqrt(x^3) + 10*x*sqrt(x^3)*log(x))/(4*x^3)
Denominador común [src] 
      10 + 5*log(x)
2*x + -------------
             ___   
         2*\/ x
2x+5log⁡(x)+102x2 x + \frac{5 \log{\left(x \right)} + 10}{2 \sqrt{x}} 
2*x + (10 + 5*log(x))/(2*sqrt(x))
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