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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
  _______     _______
\/ x + 2    \/ x - 2 
--------- + ---------
  x - 2       x + 2  
---------------------
  _______     _______
\/ x + 2    \/ x - 2 
--------- - ---------
  x - 2       x + 2
$$\frac{\frac{\sqrt{x - 2}}{x + 2} + \frac{\sqrt{x + 2}}{x - 2}}{- \frac{\sqrt{x - 2}}{x + 2} + \frac{\sqrt{x + 2}}{x - 2}}$$ 
(sqrt(x + 2)/(x - 2) + sqrt(x - 2)/(x + 2))/(sqrt(x + 2)/(x - 2) - sqrt(x - 2)/(x + 2))
Simplificación general [src] 
 /        3/2          3/2\ 
-\(-2 + x)    + (2 + x)   / 
----------------------------
          3/2          3/2  
  (-2 + x)    - (2 + x)
$$- \frac{\left(x - 2\right)^{\frac{3}{2}} + \left(x + 2\right)^{\frac{3}{2}}}{\left(x - 2\right)^{\frac{3}{2}} - \left(x + 2\right)^{\frac{3}{2}}}$$ 
-((-2 + x)^(3/2) + (2 + x)^(3/2))/((-2 + x)^(3/2) - (2 + x)^(3/2))
Respuesta numérica [src] 
(1.4142135623731*(1 + 0.5*x)^0.5/(-2.0 + x) + 1.4142135623731*(-1 + 0.5*x)^0.5/(2.0 + x))/(1.4142135623731*(1 + 0.5*x)^0.5/(-2.0 + x) - 1.4142135623731*(-1 + 0.5*x)^0.5/(2.0 + x))
(1.4142135623731*(1 + 0.5*x)^0.5/(-2.0 + x) + 1.4142135623731*(-1 + 0.5*x)^0.5/(2.0 + x))/(1.4142135623731*(1 + 0.5*x)^0.5/(-2.0 + x) - 1.4142135623731*(-1 + 0.5*x)^0.5/(2.0 + x))
Denominador común [src] 
                      ________         ________            
                - 4*\/ -2 + x  + 2*x*\/ -2 + x             
1 + -------------------------------------------------------
        ________       _______       _______       ________
    2*\/ -2 + x  + 2*\/ 2 + x  + x*\/ 2 + x  - x*\/ -2 + x
$$\frac{2 x \sqrt{x - 2} - 4 \sqrt{x - 2}}{- x \sqrt{x - 2} + x \sqrt{x + 2} + 2 \sqrt{x - 2} + 2 \sqrt{x + 2}} + 1$$ 
1 + (-4*sqrt(-2 + x) + 2*x*sqrt(-2 + x))/(2*sqrt(-2 + x) + 2*sqrt(2 + x) + x*sqrt(2 + x) - x*sqrt(-2 + x))
Unión de expresiones racionales [src] 
        3/2          3/2
(-2 + x)    + (2 + x)   
------------------------
       3/2           3/2
(2 + x)    - (-2 + x)
$$\frac{\left(x - 2\right)^{\frac{3}{2}} + \left(x + 2\right)^{\frac{3}{2}}}{- \left(x - 2\right)^{\frac{3}{2}} + \left(x + 2\right)^{\frac{3}{2}}}$$ 
((-2 + x)^(3/2) + (2 + x)^(3/2))/((2 + x)^(3/2) - (-2 + x)^(3/2))
Denominador racional [src] 
                          2
/        3/2          3/2\ 
\(-2 + x)    + (2 + x)   / 
---------------------------
                  2        
         16 + 12*x
$$\frac{\left(\left(x - 2\right)^{\frac{3}{2}} + \left(x + 2\right)^{\frac{3}{2}}\right)^{2}}{12 x^{2} + 16}$$ 
((-2 + x)^(3/2) + (2 + x)^(3/2))^2/(16 + 12*x^2)
Combinatoria [src] 
      ________       _______       ________       _______
- 2*\/ -2 + x  + 2*\/ 2 + x  + x*\/ -2 + x  + x*\/ 2 + x 
---------------------------------------------------------
     ________       _______       _______       ________ 
 2*\/ -2 + x  + 2*\/ 2 + x  + x*\/ 2 + x  - x*\/ -2 + x
$$\frac{x \sqrt{x - 2} + x \sqrt{x + 2} - 2 \sqrt{x - 2} + 2 \sqrt{x + 2}}{- x \sqrt{x - 2} + x \sqrt{x + 2} + 2 \sqrt{x - 2} + 2 \sqrt{x + 2}}$$ 
(-2*sqrt(-2 + x) + 2*sqrt(2 + x) + x*sqrt(-2 + x) + x*sqrt(2 + x))/(2*sqrt(-2 + x) + 2*sqrt(2 + x) + x*sqrt(2 + x) - x*sqrt(-2 + x))
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