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Simplificación de expresiones/ Descomposición en fracciones simples/ (((a-(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2)))-((a+(a^2-b^2)^(1/2))/(a-(a^2-b^2)^(1/2))))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
       _________          _________
      /  2    2          /  2    2 
a - \/  a  - b     a + \/  a  - b  
---------------- - ----------------
       _________          _________
      /  2    2          /  2    2 
a + \/  a  - b     a - \/  a  - b
$$\frac{a - \sqrt{a^{2} - b^{2}}}{a + \sqrt{a^{2} - b^{2}}} - \frac{a + \sqrt{a^{2} - b^{2}}}{a - \sqrt{a^{2} - b^{2}}}$$ 
(a - sqrt(a^2 - b^2))/(a + sqrt(a^2 - b^2)) - (a + sqrt(a^2 - b^2))/(a - sqrt(a^2 - b^2))
Simplificación general [src] 
        _________
       /  2    2 
-4*a*\/  a  - b  
-----------------
         2       
        b
$$- \frac{4 a \sqrt{a^{2} - b^{2}}}{b^{2}}$$ 
-4*a*sqrt(a^2 - b^2)/b^2
Respuesta numérica [src] 
(a - (a^2 - b^2)^0.5)/(a + (a^2 - b^2)^0.5) - (a + (a^2 - b^2)^0.5)/(a - (a^2 - b^2)^0.5)
(a - (a^2 - b^2)^0.5)/(a + (a^2 - b^2)^0.5) - (a + (a^2 - b^2)^0.5)/(a - (a^2 - b^2)^0.5)
Unión de expresiones racionales [src] 
                  2                     2
/       _________\    /       _________\ 
|      /  2    2 |    |      /  2    2 | 
\a - \/  a  - b  /  - \a + \/  a  - b  / 
-----------------------------------------
  /       _________\ /       _________\  
  |      /  2    2 | |      /  2    2 |  
  \a + \/  a  - b  /*\a - \/  a  - b  /
$$\frac{\left(a - \sqrt{a^{2} - b^{2}}\right)^{2} - \left(a + \sqrt{a^{2} - b^{2}}\right)^{2}}{\left(a - \sqrt{a^{2} - b^{2}}\right) \left(a + \sqrt{a^{2} - b^{2}}\right)}$$ 
((a - sqrt(a^2 - b^2))^2 - (a + sqrt(a^2 - b^2))^2)/((a + sqrt(a^2 - b^2))*(a - sqrt(a^2 - b^2)))
Denominador racional [src] 
                     2                        2
   /       _________\       /       _________\ 
 2 |      /  2    2 |     2 |      /  2    2 | 
b *\a - \/  a  - b  /  - b *\a + \/  a  - b  / 
-----------------------------------------------
                        4                      
                       b
$$\frac{b^{2} \left(a - \sqrt{a^{2} - b^{2}}\right)^{2} - b^{2} \left(a + \sqrt{a^{2} - b^{2}}\right)^{2}}{b^{4}}$$ 
(b^2*(a - sqrt(a^2 - b^2))^2 - b^2*(a + sqrt(a^2 - b^2))^2)/b^4
Combinatoria [src] 
                  _________          
                 /  2    2           
          -4*a*\/  a  - b            
-------------------------------------
/       _________\ /       _________\
|      /  2    2 | |      /  2    2 |
\a + \/  a  - b  /*\a - \/  a  - b  /
$$- \frac{4 a \sqrt{a^{2} - b^{2}}}{\left(a - \sqrt{a^{2} - b^{2}}\right) \left(a + \sqrt{a^{2} - b^{2}}\right)}$$ 
-4*a*sqrt(a^2 - b^2)/((a + sqrt(a^2 - b^2))*(a - sqrt(a^2 - b^2)))
Denominador común [src] 
        _________
       /  2    2 
-4*a*\/  a  - b  
-----------------
         2       
        b
$$- \frac{4 a \sqrt{a^{2} - b^{2}}}{b^{2}}$$ 
-4*a*sqrt(a^2 - b^2)/b^2
Potencias [src] 
       _________           _________
      /  2    2           /  2    2 
a - \/  a  - b     -a - \/  a  - b  
---------------- + -----------------
       _________           _________
      /  2    2           /  2    2 
a + \/  a  - b      a - \/  a  - b
$$\frac{- a - \sqrt{a^{2} - b^{2}}}{a - \sqrt{a^{2} - b^{2}}} + \frac{a - \sqrt{a^{2} - b^{2}}}{a + \sqrt{a^{2} - b^{2}}}$$ 
(a - sqrt(a^2 - b^2))/(a + sqrt(a^2 - b^2)) + (-a - sqrt(a^2 - b^2))/(a - sqrt(a^2 - b^2))
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