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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(2)/(sqrt(8)+2)-((6-sqrt(32))/sqrt((8)-3))

¿Cómo vas a descomponer esta sqrt(2)/(sqrt(8)+2)-((6-sqrt(32))/sqrt((8)-3)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    ___           ____
  \/ 2      6 - \/ 32 
--------- - ----------
  ___           ___   
\/ 8  + 2     \/ 5
$$- \frac{6 - \sqrt{32}}{\sqrt{5}} + \frac{\sqrt{2}}{2 + \sqrt{8}}$$ 
sqrt(2)/(sqrt(8) + 2) - (6 - sqrt(32))/sqrt(5)
Simplificación general [src] 
        ___     ___       ____
    6*\/ 5    \/ 2    4*\/ 10 
1 - ------- - ----- + --------
       5        2        5
$$- \frac{6 \sqrt{5}}{5} - \frac{\sqrt{2}}{2} + 1 + \frac{4 \sqrt{10}}{5}$$ 
1 - 6*sqrt(5)/5 - sqrt(2)/2 + 4*sqrt(10)/5
Respuesta numérica [src] 
0.139433773948408
0.139433773948408
Unión de expresiones racionales [src] 
    ___       ___ /      ___\ /        ___\
5*\/ 2  - 4*\/ 5 *\1 + \/ 2 /*\3 - 2*\/ 2 /
-------------------------------------------
                  /      ___\              
               10*\1 + \/ 2 /
$$\frac{- 4 \sqrt{5} \left(1 + \sqrt{2}\right) \left(3 - 2 \sqrt{2}\right) + 5 \sqrt{2}}{10 \left(1 + \sqrt{2}\right)}$$ 
(5*sqrt(2) - 4*sqrt(5)*(1 + sqrt(2))*(3 - 2*sqrt(2)))/(10*(1 + sqrt(2)))
Denominador común [src] 
            ___       ____
1   5 - 4*\/ 5  + 4*\/ 10 
- - ----------------------
2                 ___     
        10 + 10*\/ 2
$$- \frac{- 4 \sqrt{5} + 5 + 4 \sqrt{10}}{10 + 10 \sqrt{2}} + \frac{1}{2}$$ 
1/2 - (5 - 4*sqrt(5) + 4*sqrt(10))/(10 + 10*sqrt(2))
Combinatoria [src] 
 /      ___       ___       ____\ 
-\- 5*\/ 2  - 4*\/ 5  + 4*\/ 10 / 
----------------------------------
             /      ___\          
          10*\1 + \/ 2 /
$$- \frac{- 4 \sqrt{5} - 5 \sqrt{2} + 4 \sqrt{10}}{10 \left(1 + \sqrt{2}\right)}$$ 
-(-5*sqrt(2) - 4*sqrt(5) + 4*sqrt(10))/(10*(1 + sqrt(2)))
Potencias [src] 
     ___            /          ___\
   \/ 2         ___ |  6   4*\/ 2 |
----------- + \/ 5 *|- - + -------|
        ___         \  5      5   /
2 + 2*\/ 2
$$\sqrt{5} \left(- \frac{6}{5} + \frac{4 \sqrt{2}}{5}\right) + \frac{\sqrt{2}}{2 + 2 \sqrt{2}}$$ 
     ___        ___ /        ___\
   \/ 2       \/ 5 *\6 - 4*\/ 2 /
----------- - -------------------
        ___            5         
2 + 2*\/ 2
$$- \frac{\sqrt{5} \left(6 - 4 \sqrt{2}\right)}{5} + \frac{\sqrt{2}}{2 + 2 \sqrt{2}}$$ 
sqrt(2)/(2 + 2*sqrt(2)) - sqrt(5)*(6 - 4*sqrt(2))/5
Denominador racional [src] 
          ___       ___       ____
10 - 12*\/ 5  - 5*\/ 2  + 8*\/ 10 
----------------------------------
                10
$$\frac{- 12 \sqrt{5} - 5 \sqrt{2} + 10 + 8 \sqrt{10}}{10}$$ 
(10 - 12*sqrt(5) - 5*sqrt(2) + 8*sqrt(10))/10
Parte trigonométrica [src] 
     ___        ___ /        ___\
   \/ 2       \/ 5 *\6 - 4*\/ 2 /
----------- - -------------------
        ___            5         
2 + 2*\/ 2
$$- \frac{\sqrt{5} \left(6 - 4 \sqrt{2}\right)}{5} + \frac{\sqrt{2}}{2 + 2 \sqrt{2}}$$ 
sqrt(2)/(2 + 2*sqrt(2)) - sqrt(5)*(6 - 4*sqrt(2))/5
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