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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
          /     ___                 \         /  ___\
  _______ |   \/ x           /  ___\|   x*asin\\/ x /
\/ x - 1 *|----------- + asin\\/ x /| + -------------
          |    _______              |        _______ 
          \2*\/ 1 - x               /    2*\/ x - 1
xasin⁡(x)2x−1+x−1(x21−x+asin⁡(x))\frac{x \operatorname{asin}{\left(\sqrt{x} \right)}}{2 \sqrt{x - 1}} + \sqrt{x - 1} \left(\frac{\sqrt{x}}{2 \sqrt{1 - x}} + \operatorname{asin}{\left(\sqrt{x} \right)}\right) 
sqrt(x - 1)*(sqrt(x)/((2*sqrt(1 - x))) + asin(sqrt(x))) + (x*asin(sqrt(x)))/((2*sqrt(x - 1)))
Simplificación general [src] 
         /  ___       _______     /  ___\\       _______     /  ___\
(-1 + x)*\\/ x  + 2*\/ 1 - x *asin\\/ x // + x*\/ 1 - x *asin\\/ x /
--------------------------------------------------------------------
                           _______   ________                       
                       2*\/ 1 - x *\/ -1 + x
x1−xasin⁡(x)+(x+21−xasin⁡(x))(x−1)21−xx−1\frac{x \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)} + \left(\sqrt{x} + 2 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}\right) \left(x - 1\right)}{2 \sqrt{1 - x} \sqrt{x - 1}} 
((-1 + x)*(sqrt(x) + 2*sqrt(1 - x)*asin(sqrt(x))) + x*sqrt(1 - x)*asin(sqrt(x)))/(2*sqrt(1 - x)*sqrt(-1 + x))
Denominador racional [src] 
      /  ___\            /  ___\      3/2   _______       ___   _______      2     /  ___\
4*asin\\/ x / - 10*x*asin\\/ x / - 2*x   *\/ 1 - x  + 2*\/ x *\/ 1 - x  + 6*x *asin\\/ x /
------------------------------------------------------------------------------------------
                                                3/2                                       
                                      4*(-1 + x)
−2x321−x+2x1−x+6x2asin⁡(x)−10xasin⁡(x)+4asin⁡(x)4(x−1)32\frac{- 2 x^{\frac{3}{2}} \sqrt{1 - x} + 2 \sqrt{x} \sqrt{1 - x} + 6 x^{2} \operatorname{asin}{\left(\sqrt{x} \right)} - 10 x \operatorname{asin}{\left(\sqrt{x} \right)} + 4 \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \left(x - 1\right)^{\frac{3}{2}}} 
(4*asin(sqrt(x)) - 10*x*asin(sqrt(x)) - 2*x^(3/2)*sqrt(1 - x) + 2*sqrt(x)*sqrt(1 - x) + 6*x^2*asin(sqrt(x)))/(4*(-1 + x)^(3/2))
Denominador común [src] 
 3/2     ___       _______     /  ___\         _______     /  ___\
x    - \/ x  - 2*\/ 1 - x *asin\\/ x / + 3*x*\/ 1 - x *asin\\/ x /
------------------------------------------------------------------
                          _______   ________                      
                      2*\/ 1 - x *\/ -1 + x
x32−x+3x1−xasin⁡(x)−21−xasin⁡(x)21−xx−1\frac{x^{\frac{3}{2}} - \sqrt{x} + 3 x \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)} - 2 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}}{2 \sqrt{1 - x} \sqrt{x - 1}} 
(x^(3/2) - sqrt(x) - 2*sqrt(1 - x)*asin(sqrt(x)) + 3*x*sqrt(1 - x)*asin(sqrt(x)))/(2*sqrt(1 - x)*sqrt(-1 + x))
Combinatoria [src] 
 3/2     ___       _______     /  ___\         _______     /  ___\
x    - \/ x  - 2*\/ 1 - x *asin\\/ x / + 3*x*\/ 1 - x *asin\\/ x /
------------------------------------------------------------------
                          _______   ________                      
                      2*\/ 1 - x *\/ -1 + x
x32−x+3x1−xasin⁡(x)−21−xasin⁡(x)21−xx−1\frac{x^{\frac{3}{2}} - \sqrt{x} + 3 x \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)} - 2 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}}{2 \sqrt{1 - x} \sqrt{x - 1}} 
(x^(3/2) - sqrt(x) - 2*sqrt(1 - x)*asin(sqrt(x)) + 3*x*sqrt(1 - x)*asin(sqrt(x)))/(2*sqrt(1 - x)*sqrt(-1 + x))
Unión de expresiones racionales [src] 
         /  ___       _______     /  ___\\       _______     /  ___\
(-1 + x)*\\/ x  + 2*\/ 1 - x *asin\\/ x // + x*\/ 1 - x *asin\\/ x /
--------------------------------------------------------------------
                           _______   ________                       
                       2*\/ 1 - x *\/ -1 + x
x1−xasin⁡(x)+(x+21−xasin⁡(x))(x−1)21−xx−1\frac{x \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)} + \left(\sqrt{x} + 2 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}\right) \left(x - 1\right)}{2 \sqrt{1 - x} \sqrt{x - 1}} 
((-1 + x)*(sqrt(x) + 2*sqrt(1 - x)*asin(sqrt(x))) + x*sqrt(1 - x)*asin(sqrt(x)))/(2*sqrt(1 - x)*sqrt(-1 + x))
Respuesta numérica [src] 
(-1.0 + x)^0.5*(0.5*x^0.5*(1.0 - x)^(-0.5) + asin(sqrt(x))) + 0.5*x*(-1.0 + x)^(-0.5)*asin(sqrt(x))
(-1.0 + x)^0.5*(0.5*x^0.5*(1.0 - x)^(-0.5) + asin(sqrt(x))) + 0.5*x*(-1.0 + x)^(-0.5)*asin(sqrt(x))
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