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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(2)/(1-x^2)+2^(3/2)/(x^(-2)/(1/(x^2*(1+x^(-2)))))

¿Cómo vas a descomponer esta sqrt(2)/(1-x^2)+2^(3/2)/(x^(-2)/(1/(x^2*(1+x^(-2))))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  ___           3/2      
\/ 2           2         
------ + ----------------
     2   /      1       \
1 - x    |--------------|
         | 2      1     |
         |x *-----------|
         |    2 /    1 \|
         |   x *|1 + --||
         |      |     2||
         \      \    x //
$$\frac{\sqrt{2}}{1 - x^{2}} + \frac{2^{\frac{3}{2}}}{\frac{1}{x^{2}} \frac{1}{\frac{1}{x^{2} \left(1 + \frac{1}{x^{2}}\right)}}}$$ 
sqrt(2)/(1 - x^2) + 2^(3/2)/((1/(x^2*1/(x^2*(1 + x^(-2))))))
Descomposición de una fracción [src] 
2*sqrt(2) + sqrt(2)/(2*(1 + x)) - 2*sqrt(2)/(1 + x^2) - sqrt(2)/(2*(-1 + x))
$$2 \sqrt{2} - \frac{2 \sqrt{2}}{x^{2} + 1} + \frac{\sqrt{2}}{2 \left(x + 1\right)} - \frac{\sqrt{2}}{2 \left(x - 1\right)}$$ 
              ___         ___       ___   
    ___     \/ 2      2*\/ 2      \/ 2    
2*\/ 2  + --------- - ------- - ----------
          2*(1 + x)         2   2*(-1 + x)
                       1 + x
Simplificación general [src] 
  ___ /        2      4\
\/ 2 *\-1 - 3*x  + 2*x /
------------------------
              4         
        -1 + x
$$\frac{\sqrt{2} \left(2 x^{4} - 3 x^{2} - 1\right)}{x^{4} - 1}$$ 
sqrt(2)*(-1 - 3*x^2 + 2*x^4)/(-1 + x^4)
Respuesta numérica [src] 
1.4142135623731/(1.0 - x^2) + 2.82842712474619/(1.0 + x^(-2))
1.4142135623731/(1.0 - x^2) + 2.82842712474619/(1.0 + x^(-2))
Combinatoria [src] 
   ___ /        2      4\
 \/ 2 *\-1 - 3*x  + 2*x /
-------------------------
        /     2\         
(1 + x)*\1 + x /*(-1 + x)
$$\frac{\sqrt{2} \left(2 x^{4} - 3 x^{2} - 1\right)}{\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)}$$ 
sqrt(2)*(-1 - 3*x^2 + 2*x^4)/((1 + x)*(1 + x^2)*(-1 + x))
Denominador racional [src] 
  ___  2 /     2\       ___  4 /     2\
\/ 2 *x *\1 + x / + 2*\/ 2 *x *\1 - x /
---------------------------------------
           2 /     2\ /     2\         
          x *\1 + x /*\1 - x /
$$\frac{2 \sqrt{2} x^{4} \left(1 - x^{2}\right) + \sqrt{2} x^{2} \left(x^{2} + 1\right)}{x^{2} \left(1 - x^{2}\right) \left(x^{2} + 1\right)}$$ 
(sqrt(2)*x^2*(1 + x^2) + 2*sqrt(2)*x^4*(1 - x^2))/(x^2*(1 + x^2)*(1 - x^2))
Abrimos la expresión [src] 
  ___        ___
\/ 2     2*\/ 2 
------ + -------
     2        1 
1 - x     1 + --
               2
              x
$$\frac{\sqrt{2}}{1 - x^{2}} + \frac{2 \sqrt{2}}{1 + \frac{1}{x^{2}}}$$ 
sqrt(2)/(1 - x^2) + 2*sqrt(2)/(1 + x^(-2))
Parte trigonométrica [src] 
  ___        ___
\/ 2     2*\/ 2 
------ + -------
     2        1 
1 - x     1 + --
               2
              x
$$\frac{\sqrt{2}}{1 - x^{2}} + \frac{2 \sqrt{2}}{1 + \frac{1}{x^{2}}}$$ 
sqrt(2)/(1 - x^2) + 2*sqrt(2)/(1 + x^(-2))
Unión de expresiones racionales [src] 
  ___ /     2      2 /     2\\
\/ 2 *\1 + x  + 2*x *\1 - x //
------------------------------
      /     2\ /     2\       
      \1 + x /*\1 - x /
$$\frac{\sqrt{2} \left(2 x^{2} \left(1 - x^{2}\right) + x^{2} + 1\right)}{\left(1 - x^{2}\right) \left(x^{2} + 1\right)}$$ 
sqrt(2)*(1 + x^2 + 2*x^2*(1 - x^2))/((1 + x^2)*(1 - x^2))
Compilar la expresión [src] 
  ___        ___
\/ 2     2*\/ 2 
------ + -------
     2        1 
1 - x     1 + --
               2
              x
$$\frac{\sqrt{2}}{1 - x^{2}} + \frac{2 \sqrt{2}}{1 + \frac{1}{x^{2}}}$$ 
sqrt(2)/(1 - x^2) + 2*sqrt(2)/(1 + x^(-2))
Denominador común [src] 
              ___       ___  2
    ___   - \/ 2  + 3*\/ 2 *x 
2*\/ 2  - --------------------
                      4       
                -1 + x
$$2 \sqrt{2} - \frac{3 \sqrt{2} x^{2} - \sqrt{2}}{x^{4} - 1}$$ 
2*sqrt(2) - (-sqrt(2) + 3*sqrt(2)*x^2)/(-1 + x^4)
Potencias [src] 
  ___        ___
\/ 2     2*\/ 2 
------ + -------
     2        1 
1 - x     1 + --
               2
              x
$$\frac{\sqrt{2}}{1 - x^{2}} + \frac{2 \sqrt{2}}{1 + \frac{1}{x^{2}}}$$ 
sqrt(2)/(1 - x^2) + 2*sqrt(2)/(1 + x^(-2))
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