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

Expresión a simplificar:

Solución

Ha introducido [src]
   ________                                
  /      2                           2     
\/  1 - x           1               x      
----------- + ------------- - -------------
     2             ________        ________
                  /      2        /      2 
              2*\/  1 - x     2*\/  1 - x  
$$- \frac{x^{2}}{2 \sqrt{1 - x^{2}}} + \left(\frac{\sqrt{1 - x^{2}}}{2} + \frac{1}{2 \sqrt{1 - x^{2}}}\right)$$
sqrt(1 - x^2)/2 + 1/(2*sqrt(1 - x^2)) - x^2/(2*sqrt(1 - x^2))
Simplificación general [src]
   ________
  /      2 
\/  1 - x  
$$\sqrt{1 - x^{2}}$$
sqrt(1 - x^2)
Respuesta numérica [src]
0.5*(1.0 - x^2)^0.5 + 0.5*(1.0 - x^2)^(-0.5) - 0.5*x^2*(1.0 - x^2)^(-0.5)
0.5*(1.0 - x^2)^0.5 + 0.5*(1.0 - x^2)^(-0.5) - 0.5*x^2*(1.0 - x^2)^(-0.5)
Denominador racional [src]
          ________        ________           
     2   /      2        /      2  /       2\
- 4*x *\/  1 - x   + 2*\/  1 - x  *\4 - 2*x /
---------------------------------------------
                          2                  
                   8 - 8*x                   
$$\frac{- 4 x^{2} \sqrt{1 - x^{2}} + 2 \sqrt{1 - x^{2}} \left(4 - 2 x^{2}\right)}{8 - 8 x^{2}}$$
(-4*x^2*sqrt(1 - x^2) + 2*sqrt(1 - x^2)*(4 - 2*x^2))/(8 - 8*x^2)
Abrimos la expresión [src]
                   ________                
                  /      2           2     
      1         \/  1 - x           x      
------------- + ----------- - -------------
     ________        2             ________
    /      2                      /      2 
2*\/  1 - x                   2*\/  1 - x  
$$- \frac{x^{2}}{2 \sqrt{1 - x^{2}}} + \frac{\sqrt{1 - x^{2}}}{2} + \frac{1}{2 \sqrt{1 - x^{2}}}$$
1/(2*sqrt(1 - x^2)) + sqrt(1 - x^2)/2 - x^2/(2*sqrt(1 - x^2))
Compilar la expresión [src]
   ________                                
  /      2                           2     
\/  1 - x           1               x      
----------- + ------------- - -------------
     2             ________        ________
                  /      2        /      2 
              2*\/  1 - x     2*\/  1 - x  
$$- \frac{x^{2}}{2 \sqrt{1 - x^{2}}} + \frac{\sqrt{1 - x^{2}}}{2} + \frac{1}{2 \sqrt{1 - x^{2}}}$$
sqrt(1 - x^2)/2 + 1/(2*sqrt(1 - x^2)) - x^2/(2*sqrt(1 - x^2))
Denominador común [src]
   ________
  /      2 
\/  1 - x  
$$\sqrt{1 - x^{2}}$$
sqrt(1 - x^2)
Combinatoria [src]
  ___________________
\/ -(1 + x)*(-1 + x) 
$$\sqrt{- \left(x - 1\right) \left(x + 1\right)}$$
sqrt(-(1 + x)*(-1 + x))
Unión de expresiones racionales [src]
   ________
  /      2 
\/  1 - x  
$$\sqrt{1 - x^{2}}$$
sqrt(1 - x^2)
Parte trigonométrica [src]
   ________                                
  /      2                           2     
\/  1 - x           1               x      
----------- + ------------- - -------------
     2             ________        ________
                  /      2        /      2 
              2*\/  1 - x     2*\/  1 - x  
$$- \frac{x^{2}}{2 \sqrt{1 - x^{2}}} + \frac{\sqrt{1 - x^{2}}}{2} + \frac{1}{2 \sqrt{1 - x^{2}}}$$
sqrt(1 - x^2)/2 + 1/(2*sqrt(1 - x^2)) - x^2/(2*sqrt(1 - x^2))
Potencias [src]
   ________                                
  /      2                           2     
\/  1 - x           1               x      
----------- + ------------- - -------------
     2             ________        ________
                  /      2        /      2 
              2*\/  1 - x     2*\/  1 - x  
$$- \frac{x^{2}}{2 \sqrt{1 - x^{2}}} + \frac{\sqrt{1 - x^{2}}}{2} + \frac{1}{2 \sqrt{1 - x^{2}}}$$
sqrt(1 - x^2)/2 + 1/(2*sqrt(1 - x^2)) - x^2/(2*sqrt(1 - x^2))