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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    _______                                   
   / 1 - x          /      1         1 - x   \
  /  ----- *(1 + x)*|- --------- - ----------|
\/   1 + x          |  2*(1 + x)            2|
                    \              2*(1 + x) /
----------------------------------------------
                    1 - x
1−xx+1(x+1)(−1−x2(x+1)2−12(x+1))1−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 \left(x + 1\right)}\right)}{1 - x} 
((sqrt((1 - x)/(1 + x))*(1 + x))*(-1/(2*(1 + x)) - (1 - x)/(2*(1 + x)^2)))/(1 - x)
Simplificación general [src] 
    _______
   / 1 - x 
  /  ----- 
\/   1 + x 
-----------
        2  
  -1 + x
1−xx+1x2−1\frac{\sqrt{\frac{1 - x}{x + 1}}}{x^{2} - 1} 
sqrt((1 - x)/(1 + x))/(-1 + x^2)
Respuesta numérica [src] 
((1.0 - x)/(1.0 + x))^0.5*(1.0 + x)*(-1/(2.0 + 2.0*x) - 0.5*(1.0 - x)/(1.0 + x)^2)/(1.0 - x)
((1.0 - x)/(1.0 + x))^0.5*(1.0 + x)*(-1/(2.0 + 2.0*x) - 0.5*(1.0 - x)/(1.0 + x)^2)/(1.0 - x)
Abrimos la expresión [src] 
    _______                                   
   /   1            /      1         1 - x   \
  /  ----- *(1 + x)*|- --------- - ----------|
\/   1 + x          |  2*(1 + x)            2|
                    \              2*(1 + x) /
----------------------------------------------
                    _______                   
                  \/ 1 - x
(x+1)(−1−x2(x+1)2−12(x+1))1x+11−x\frac{\left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 \left(x + 1\right)}\right) \sqrt{\frac{1}{x + 1}}}{\sqrt{1 - x}} 
sqrt(1/(1 + x))*(1 + x)*(-1/(2*(1 + x)) - (1 - x)/(2*(1 + x)^2))/sqrt(1 - x)
Combinatoria [src] 
    ____________
   / -(-1 + x)  
  /  ---------- 
\/     1 + x    
----------------
(1 + x)*(-1 + x)
−x−1x+1(x−1)(x+1)\frac{\sqrt{- \frac{x - 1}{x + 1}}}{\left(x - 1\right) \left(x + 1\right)} 
sqrt(-(-1 + x)/(1 + x))/((1 + x)*(-1 + x))
Denominador común [src] 
    _______________
   /   1       x   
  /  ----- - ----- 
\/   1 + x   1 + x 
-------------------
            2      
      -1 + x
−xx+1+1x+1x2−1\frac{\sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}}}{x^{2} - 1} 
sqrt(1/(1 + x) - x/(1 + x))/(-1 + x^2)
Unión de expresiones racionales [src] 
      _______  
     / 1 - x   
 -  /  -----   
  \/   1 + x   
---------------
(1 + x)*(1 - x)
−1−xx+1(1−x)(x+1)- \frac{\sqrt{\frac{1 - x}{x + 1}}}{\left(1 - x\right) \left(x + 1\right)} 
-sqrt((1 - x)/(1 + x))/((1 + x)*(1 - x))
Potencias [src] 
                    /              1   x \
    _______         |            - - + - |
   / 1 - x          |     1        2   2 |
  /  ----- *(1 + x)*|- ------- + --------|
\/   1 + x          |  2 + 2*x          2|
                    \            (1 + x) /
------------------------------------------
                  1 - x
1−xx+1(x+1)(x2−12(x+1)2−12x+2)1−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(\frac{\frac{x}{2} - \frac{1}{2}}{\left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right)}{1 - x} 
    _______                                 
   / 1 - x          /     1        1 - x   \
  /  ----- *(1 + x)*|- ------- - ----------|
\/   1 + x          |  2 + 2*x            2|
                    \            2*(1 + x) /
--------------------------------------------
                   1 - x
1−xx+1(x+1)(−1−x2(x+1)2−12x+2)1−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right)}{1 - x} 
sqrt((1 - x)/(1 + x))*(1 + x)*(-1/(2 + 2*x) - (1 - x)/(2*(1 + x)^2))/(1 - x)
Parte trigonométrica [src] 
    _______                                 
   / 1 - x          /     1        1 - x   \
  /  ----- *(1 + x)*|- ------- - ----------|
\/   1 + x          |  2 + 2*x            2|
                    \            2*(1 + x) /
--------------------------------------------
                   1 - x
1−xx+1(x+1)(−1−x2(x+1)2−12x+2)1−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right)}{1 - x} 
sqrt((1 - x)/(1 + x))*(1 + x)*(-1/(2 + 2*x) - (1 - x)/(2*(1 + x)^2))/(1 - x)
Compilar la expresión [src] 
    _______                                 
   / 1 - x          /     1        1 - x   \
  /  ----- *(1 + x)*|- ------- - ----------|
\/   1 + x          |  2 + 2*x            2|
                    \            2*(1 + x) /
--------------------------------------------
                   1 - x
1−xx+1(x+1)(−1−x2(x+1)2−12x+2)1−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right)}{1 - x} 
sqrt((1 - x)/(1 + x))*(1 + x)*(-1/(2 + 2*x) - (1 - x)/(2*(1 + x)^2))/(1 - x)
Denominador racional [src] 
    _______                                    
   / 1 - x  /           2                     \
  /  ----- *\- 2*(1 + x)  + (-1 + x)*(2 + 2*x)/
\/   1 + x                                     
-----------------------------------------------
          2*(1 + x)*(1 - x)*(2 + 2*x)
1−xx+1((x−1)(2x+2)−2(x+1)2)2(1−x)(x+1)(2x+2)\frac{\sqrt{\frac{1 - x}{x + 1}} \left(\left(x - 1\right) \left(2 x + 2\right) - 2 \left(x + 1\right)^{2}\right)}{2 \left(1 - x\right) \left(x + 1\right) \left(2 x + 2\right)} 
sqrt((1 - x)/(1 + x))*(-2*(1 + x)^2 + (-1 + x)*(2 + 2*x))/(2*(1 + x)*(1 - x)*(2 + 2*x))
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