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

Expresión a simplificar:

Solución

Ha introducido [src]
    _______________ /   ________                \
   /      ________  |  /      2           2     |
  /      /      2   |\/  5 - x           x      |
\/   x*\/  5 - x   *|----------- - -------------|
                    |     2             ________|
                    |                  /      2 |
                    \              2*\/  5 - x  /
-------------------------------------------------
                       ________                  
                      /      2                   
                  x*\/  5 - x                    
$$\frac{\sqrt{x \sqrt{5 - x^{2}}} \left(- \frac{x^{2}}{2 \sqrt{5 - x^{2}}} + \frac{\sqrt{5 - x^{2}}}{2}\right)}{x \sqrt{5 - x^{2}}}$$
(sqrt(x*sqrt(5 - x^2))*(sqrt(5 - x^2)/2 - x^2/(2*sqrt(5 - x^2))))/((x*sqrt(5 - x^2)))
Simplificación general [src]
    _______________         
   /      ________          
  /      /      2   /5    2\
\/   x*\/  5 - x   *|- - x |
                    \2     /
----------------------------
           /     2\         
         x*\5 - x /         
$$\frac{\sqrt{x \sqrt{5 - x^{2}}} \left(\frac{5}{2} - x^{2}\right)}{x \left(5 - x^{2}\right)}$$
sqrt(x*sqrt(5 - x^2))*(5/2 - x^2)/(x*(5 - x^2))
Denominador común [src]
        _______________            _______________
       /      ________            /      ________ 
      /      /      2        2   /      /      2  
- 5*\/   x*\/  5 - x    + 2*x *\/   x*\/  5 - x   
--------------------------------------------------
                              3                   
                   -10*x + 2*x                    
$$\frac{2 x^{2} \sqrt{x \sqrt{5 - x^{2}}} - 5 \sqrt{x \sqrt{5 - x^{2}}}}{2 x^{3} - 10 x}$$
(-5*sqrt(x*sqrt(5 - x^2)) + 2*x^2*sqrt(x*sqrt(5 - x^2)))/(-10*x + 2*x^3)
Respuesta numérica [src]
0.668740304976422*(x*(1 - 0.2*x^2)^0.5)^0.5*(1 - 0.2*x^2)^(-0.5)*(1.11803398874989*(1 - 0.2*x^2)^0.5 - 0.223606797749979*x^2*(1 - 0.2*x^2)^(-0.5))/x
0.668740304976422*(x*(1 - 0.2*x^2)^0.5)^0.5*(1 - 0.2*x^2)^(-0.5)*(1.11803398874989*(1 - 0.2*x^2)^0.5 - 0.223606797749979*x^2*(1 - 0.2*x^2)^(-0.5))/x
Abrimos la expresión [src]
   ________                
  /      2           2     
\/  5 - x           x      
----------- - -------------
     2             ________
                  /      2 
              2*\/  5 - x  
---------------------------
              ________     
       ___ 4 /      2      
     \/ x *\/  5 - x       
$$\frac{- \frac{x^{2}}{2 \sqrt{5 - x^{2}}} + \frac{\sqrt{5 - x^{2}}}{2}}{\sqrt{x} \sqrt[4]{5 - x^{2}}}$$
(sqrt(5 - x^2)/2 - x^2/(2*sqrt(5 - x^2)))/(sqrt(x)*(5 - x^2)^(1/4))
Combinatoria [src]
    _______________            
   /      ________             
  /      /      2   /        2\
\/   x*\/  5 - x   *\-5 + 2*x /
-------------------------------
             /      2\         
         2*x*\-5 + x /         
$$\frac{\sqrt{x \sqrt{5 - x^{2}}} \left(2 x^{2} - 5\right)}{2 x \left(x^{2} - 5\right)}$$
sqrt(x*sqrt(5 - x^2))*(-5 + 2*x^2)/(2*x*(-5 + x^2))
Denominador racional [src]
    _______________            
   /      ________             
  /      /      2   /        2\
\/   x*\/  5 - x   *\10 - 4*x /
-------------------------------
              /     2\         
          4*x*\5 - x /         
$$\frac{\sqrt{x \sqrt{5 - x^{2}}} \left(10 - 4 x^{2}\right)}{4 x \left(5 - x^{2}\right)}$$
sqrt(x*sqrt(5 - x^2))*(10 - 4*x^2)/(4*x*(5 - x^2))
Unión de expresiones racionales [src]
    _______________           
   /      ________            
  /      /      2   /       2\
\/   x*\/  5 - x   *\5 - 2*x /
------------------------------
             /     2\         
         2*x*\5 - x /         
$$\frac{\sqrt{x \sqrt{5 - x^{2}}} \left(5 - 2 x^{2}\right)}{2 x \left(5 - x^{2}\right)}$$
sqrt(x*sqrt(5 - x^2))*(5 - 2*x^2)/(2*x*(5 - x^2))