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Simplificación de expresiones/ Descomposición en fracciones simples/ asin(sqrt(x))+(x-(1/2))/(2*sqrt(x-x^2))-x/(2*sqrt(x-x^2))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    /  ___\      x - 1/2            x      
asin\\/ x / + ------------- - -------------
                   ________        ________
                  /      2        /      2 
              2*\/  x - x     2*\/  x - x
−x2−x2+x+(x−122−x2+x+asin⁡(x))- \frac{x}{2 \sqrt{- x^{2} + x}} + \left(\frac{x - \frac{1}{2}}{2 \sqrt{- x^{2} + x}} + \operatorname{asin}{\left(\sqrt{x} \right)}\right) 
asin(sqrt(x)) + (x - 1/2)/((2*sqrt(x - x^2))) - x/(2*sqrt(x - x^2))
Simplificación general [src] 
        1             /  ___\
- ------------- + asin\\/ x /
       ________              
      /      2               
  4*\/  x - x
asin⁡(x)−14−x2+x\operatorname{asin}{\left(\sqrt{x} \right)} - \frac{1}{4 \sqrt{- x^{2} + x}} 
-1/(4*sqrt(x - x^2)) + asin(sqrt(x))
Respuesta numérica [src] 
0.5*(x - x^2)^(-0.5)*(-0.5 + x) - 0.5*x*(x - x^2)^(-0.5) + asin(sqrt(x))
0.5*(x - x^2)^(-0.5)*(-0.5 + x) - 0.5*x*(x - x^2)^(-0.5) + asin(sqrt(x))
Denominador común [src] 
        1             /  ___\
- ------------- + asin\\/ x /
       ________              
      /      2               
  4*\/  x - x
asin⁡(x)−14−x2+x\operatorname{asin}{\left(\sqrt{x} \right)} - \frac{1}{4 \sqrt{- x^{2} + x}} 
-1/(4*sqrt(x - x^2)) + asin(sqrt(x))
Denominador racional [src] 
         ________        ________ /                ________            \
        /      2        /      2  |               /      2      /  ___\|
- 4*x*\/  x - x   + 2*\/  x - x  *\-1 + 2*x + 4*\/  x - x  *asin\\/ x //
------------------------------------------------------------------------
                                   2                                    
                              - 8*x  + 8*x
−4x−x2+x+2−x2+x(2x+4−x2+xasin⁡(x)−1)−8x2+8x\frac{- 4 x \sqrt{- x^{2} + x} + 2 \sqrt{- x^{2} + x} \left(2 x + 4 \sqrt{- x^{2} + x} \operatorname{asin}{\left(\sqrt{x} \right)} - 1\right)}{- 8 x^{2} + 8 x} 
(-4*x*sqrt(x - x^2) + 2*sqrt(x - x^2)*(-1 + 2*x + 4*sqrt(x - x^2)*asin(sqrt(x))))/(-8*x^2 + 8*x)
Abrimos la expresión [src] 
   x - 1/2            x             /  ___\
------------- - ------------- + asin\\/ x /
     ________        ________              
    /      2        /      2               
2*\/  x - x     2*\/  x - x
−x2−x2+x+x−122−x2+x+asin⁡(x)- \frac{x}{2 \sqrt{- x^{2} + x}} + \frac{x - \frac{1}{2}}{2 \sqrt{- x^{2} + x}} + \operatorname{asin}{\left(\sqrt{x} \right)} 
(x - 1/2)/(2*sqrt(x - x^2)) - x/(2*sqrt(x - x^2)) + asin(sqrt(x))
Compilar la expresión [src] 
   -1/2 + x           x             /  ___\
------------- - ------------- + asin\\/ x /
     ________        ________              
    /      2        /      2               
2*\/  x - x     2*\/  x - x
−x2−x2+x+x−122−x2+x+asin⁡(x)- \frac{x}{2 \sqrt{- x^{2} + x}} + \frac{x - \frac{1}{2}}{2 \sqrt{- x^{2} + x}} + \operatorname{asin}{\left(\sqrt{x} \right)} 
(-1/2 + x)/(2*sqrt(x - x^2)) - x/(2*sqrt(x - x^2)) + asin(sqrt(x))
Potencias [src] 
   -1/2 + x           x             /  ___\
------------- - ------------- + asin\\/ x /
     ________        ________              
    /      2        /      2               
2*\/  x - x     2*\/  x - x
−x2−x2+x+x−122−x2+x+asin⁡(x)- \frac{x}{2 \sqrt{- x^{2} + x}} + \frac{x - \frac{1}{2}}{2 \sqrt{- x^{2} + x}} + \operatorname{asin}{\left(\sqrt{x} \right)} 
    1   x                                
  - - + -                                
    4   2           x             /  ___\
----------- - ------------- + asin\\/ x /
   ________        ________              
  /      2        /      2               
\/  x - x     2*\/  x - x
−x2−x2+x+x2−14−x2+x+asin⁡(x)- \frac{x}{2 \sqrt{- x^{2} + x}} + \frac{\frac{x}{2} - \frac{1}{4}}{\sqrt{- x^{2} + x}} + \operatorname{asin}{\left(\sqrt{x} \right)} 
(-1/4 + x/2)/sqrt(x - x^2) - x/(2*sqrt(x - x^2)) + asin(sqrt(x))
Combinatoria [src] 
          ________            
         /      2      /  ___\
-1 + 4*\/  x - x  *asin\\/ x /
------------------------------
          _____________       
      4*\/ -x*(-1 + x)
4−x2+xasin⁡(x)−14−x(x−1)\frac{4 \sqrt{- x^{2} + x} \operatorname{asin}{\left(\sqrt{x} \right)} - 1}{4 \sqrt{- x \left(x - 1\right)}} 
(-1 + 4*sqrt(x - x^2)*asin(sqrt(x)))/(4*sqrt(-x*(-1 + x)))
Parte trigonométrica [src] 
   -1/2 + x           x             /  ___\
------------- - ------------- + asin\\/ x /
     ________        ________              
    /      2        /      2               
2*\/  x - x     2*\/  x - x
−x2−x2+x+x−122−x2+x+asin⁡(x)- \frac{x}{2 \sqrt{- x^{2} + x}} + \frac{x - \frac{1}{2}}{2 \sqrt{- x^{2} + x}} + \operatorname{asin}{\left(\sqrt{x} \right)} 
(-1/2 + x)/(2*sqrt(x - x^2)) - x/(2*sqrt(x - x^2)) + asin(sqrt(x))
Unión de expresiones racionales [src] 
         ___________     /  ___\
-1 + 4*\/ x*(1 - x) *asin\\/ x /
--------------------------------
            ___________         
        4*\/ x*(1 - x)
4x(1−x)asin⁡(x)−14x(1−x)\frac{4 \sqrt{x \left(1 - x\right)} \operatorname{asin}{\left(\sqrt{x} \right)} - 1}{4 \sqrt{x \left(1 - x\right)}} 
(-1 + 4*sqrt(x*(1 - x))*asin(sqrt(x)))/(4*sqrt(x*(1 - x)))
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