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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt((1-2*t*t)/(1-t^4))*(1-t^4)*(-2*t/(1-t^4)+2*t^3*(1-2*t*t)/(1-t^4)^2)/(1-2*t*t)

¿Cómo vas a descomponer esta sqrt((1-2*t*t)/(1-t^4))*(1-t^4)*(-2*t/(1-t^4)+2*t^3*(1-2*t*t)/(1-t^4)^2)/(1-2*t*t) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     ___________          /            3            \
    / 1 - 2*t*t  /     4\ | -2*t    2*t *(1 - 2*t*t)|
   /  --------- *\1 - t /*|------ + ----------------|
  /          4            |     4              2    |
\/      1 - t             |1 - t       /     4\     |
                          \            \1 - t /     /
-----------------------------------------------------
                      1 - 2*t*t
$$\frac{\sqrt{\frac{- t 2 t + 1}{1 - t^{4}}} \left(1 - t^{4}\right) \left(\frac{\left(-1\right) 2 t}{1 - t^{4}} + \frac{2 t^{3} \left(- t 2 t + 1\right)}{\left(1 - t^{4}\right)^{2}}\right)}{- t 2 t + 1}$$ 
((sqrt((1 - 2*t*t)/(1 - t^4))*(1 - t^4))*((-2*t)/(1 - t^4) + ((2*t^3)*(1 - 2*t*t))/(1 - t^4)^2))/(1 - 2*t*t)
Simplificación general [src] 
           ___________              
          /         2               
         /  -1 + 2*t   /     4    2\
-2*t*   /   --------- *\1 + t  - t /
       /           4                
     \/      -1 + t                 
------------------------------------
             4      2      6        
        1 - t  - 2*t  + 2*t
$$- \frac{2 t \sqrt{\frac{2 t^{2} - 1}{t^{4} - 1}} \left(t^{4} - t^{2} + 1\right)}{2 t^{6} - t^{4} - 2 t^{2} + 1}$$ 
-2*t*sqrt((-1 + 2*t^2)/(-1 + t^4))*(1 + t^4 - t^2)/(1 - t^4 - 2*t^2 + 2*t^6)
Respuesta numérica [src] 
((1.0 - 2.0*t^2)/(1.0 - t^4))^0.5*(1.0 - t^4)*(-2.0*t/(1.0 - t^4) + 2.0*t^3*(1.0 - 2.0*t^2)/(1.0 - t^4)^2)/(1.0 - 2.0*t^2)
((1.0 - 2.0*t^2)/(1.0 - t^4))^0.5*(1.0 - t^4)*(-2.0*t/(1.0 - t^4) + 2.0*t^3*(1.0 - 2.0*t^2)/(1.0 - t^4)^2)/(1.0 - 2.0*t^2)
Combinatoria [src] 
           _______________              
          /  /        2\                
         /  -\-1 + 2*t /   /     4    2\
-2*t*   /   ------------- *\1 + t  - t /
       /             4                  
     \/         1 - t                   
----------------------------------------
         /     2\          /        2\  
 (1 + t)*\1 + t /*(-1 + t)*\-1 + 2*t /
$$- \frac{2 t \sqrt{- \frac{2 t^{2} - 1}{1 - t^{4}}} \left(t^{4} - t^{2} + 1\right)}{\left(t - 1\right) \left(t + 1\right) \left(t^{2} + 1\right) \left(2 t^{2} - 1\right)}$$ 
-2*t*sqrt(-(-1 + 2*t^2)/(1 - t^4))*(1 + t^4 - t^2)/((1 + t)*(1 + t^2)*(-1 + t)*(-1 + 2*t^2))
Denominador común [src] 
 /             _________________             _________________              _________________\ 
 |            /              2              /              2               /              2  | 
 |     3     /    1       2*t              /    1       2*t         5     /    1       2*t   | 
-|- 2*t *   /   ------ - ------  + 2*t*   /   ------ - ------  + 2*t *   /   ------ - ------ | 
 |         /         4        4          /         4        4           /         4        4 | 
 \       \/     1 - t    1 - t         \/     1 - t    1 - t          \/     1 - t    1 - t  / 
-----------------------------------------------------------------------------------------------
                                           4      2      6                                     
                                      1 - t  - 2*t  + 2*t
$$- \frac{2 t^{5} \sqrt{- \frac{2 t^{2}}{1 - t^{4}} + \frac{1}{1 - t^{4}}} - 2 t^{3} \sqrt{- \frac{2 t^{2}}{1 - t^{4}} + \frac{1}{1 - t^{4}}} + 2 t \sqrt{- \frac{2 t^{2}}{1 - t^{4}} + \frac{1}{1 - t^{4}}}}{2 t^{6} - t^{4} - 2 t^{2} + 1}$$ 
-(-2*t^3*sqrt(1/(1 - t^4) - 2*t^2/(1 - t^4)) + 2*t*sqrt(1/(1 - t^4) - 2*t^2/(1 - t^4)) + 2*t^5*sqrt(1/(1 - t^4) - 2*t^2/(1 - t^4)))/(1 - t^4 - 2*t^2 + 2*t^6)
Unión de expresiones racionales [src] 
          __________                          
         /        2                           
        /  1 - 2*t   /      4    2 /       2\\
2*t*   /   -------- *\-1 + t  + t *\1 - 2*t //
      /          4                            
    \/      1 - t                             
----------------------------------------------
             /     4\ /       2\              
             \1 - t /*\1 - 2*t /
$$\frac{2 t \sqrt{\frac{1 - 2 t^{2}}{1 - t^{4}}} \left(t^{4} + t^{2} \left(1 - 2 t^{2}\right) - 1\right)}{\left(1 - 2 t^{2}\right) \left(1 - t^{4}\right)}$$ 
2*t*sqrt((1 - 2*t^2)/(1 - t^4))*(-1 + t^4 + t^2*(1 - 2*t^2))/((1 - t^4)*(1 - 2*t^2))
Denominador racional [src] 
             _____________________              _____________________              _____________________              _____________________                        _____________________
            /                  2               /                  2               /                  2               /                  2                  2      /                  2  
     9     /       1        2*t         3     /       1        2*t         7     /       1        2*t         5     /       1        2*t          /      4\      /       1        2*t   
- 4*t *   /   - ------- + -------  - 2*t *   /   - ------- + -------  + 2*t *   /   - ------- + -------  + 4*t *   /   - ------- + -------  + 2*t*\-1 + t / *   /   - ------- + ------- 
         /            4         4           /            4         4           /            4         4           /            4         4                     /            4         4 
       \/       -1 + t    -1 + t          \/       -1 + t    -1 + t          \/       -1 + t    -1 + t          \/       -1 + t    -1 + t                    \/       -1 + t    -1 + t  
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                          2                                                                                             
                                                                                 /      4\  /        2\                                                                                 
                                                                                 \-1 + t / *\-1 + 2*t /
$$\frac{- 4 t^{9} \sqrt{\frac{2 t^{2}}{t^{4} - 1} - \frac{1}{t^{4} - 1}} + 2 t^{7} \sqrt{\frac{2 t^{2}}{t^{4} - 1} - \frac{1}{t^{4} - 1}} + 4 t^{5} \sqrt{\frac{2 t^{2}}{t^{4} - 1} - \frac{1}{t^{4} - 1}} - 2 t^{3} \sqrt{\frac{2 t^{2}}{t^{4} - 1} - \frac{1}{t^{4} - 1}} + 2 t \left(t^{4} - 1\right)^{2} \sqrt{\frac{2 t^{2}}{t^{4} - 1} - \frac{1}{t^{4} - 1}}}{\left(2 t^{2} - 1\right) \left(t^{4} - 1\right)^{2}}$$ 
(-4*t^9*sqrt(-1/(-1 + t^4) + 2*t^2/(-1 + t^4)) - 2*t^3*sqrt(-1/(-1 + t^4) + 2*t^2/(-1 + t^4)) + 2*t^7*sqrt(-1/(-1 + t^4) + 2*t^2/(-1 + t^4)) + 4*t^5*sqrt(-1/(-1 + t^4) + 2*t^2/(-1 + t^4)) + 2*t*(-1 + t^4)^2*sqrt(-1/(-1 + t^4) + 2*t^2/(-1 + t^4)))/((-1 + t^4)^2*(-1 + 2*t^2))
Parte trigonométrica [src] 
      __________                                      
     /        2           /              3 /       2\\
    /  1 - 2*t   /     4\ |   2*t     2*t *\1 - 2*t /|
   /   -------- *\1 - t /*|- ------ + ---------------|
  /          4            |       4              2   |
\/      1 - t             |  1 - t       /     4\    |
                          \              \1 - t /    /
------------------------------------------------------
                              2                       
                       1 - 2*t
$$\frac{\sqrt{\frac{1 - 2 t^{2}}{1 - t^{4}}} \left(1 - t^{4}\right) \left(\frac{2 t^{3} \left(1 - 2 t^{2}\right)}{\left(1 - t^{4}\right)^{2}} - \frac{2 t}{1 - t^{4}}\right)}{1 - 2 t^{2}}$$ 
sqrt((1 - 2*t^2)/(1 - t^4))*(1 - t^4)*(-2*t/(1 - t^4) + 2*t^3*(1 - 2*t^2)/(1 - t^4)^2)/(1 - 2*t^2)
Compilar la expresión [src] 
      __________                                      
     /        2           /              3 /       2\\
    /  1 - 2*t   /     4\ |   2*t     2*t *\1 - 2*t /|
   /   -------- *\1 - t /*|- ------ + ---------------|
  /          4            |       4              2   |
\/      1 - t             |  1 - t       /     4\    |
                          \              \1 - t /    /
------------------------------------------------------
                              2                       
                       1 - 2*t
$$\frac{\sqrt{\frac{1 - 2 t^{2}}{1 - t^{4}}} \left(1 - t^{4}\right) \left(\frac{2 t^{3} \left(1 - 2 t^{2}\right)}{\left(1 - t^{4}\right)^{2}} - \frac{2 t}{1 - t^{4}}\right)}{1 - 2 t^{2}}$$ 
sqrt((1 - 2*t^2)/(1 - t^4))*(1 - t^4)*(-2*t/(1 - t^4) + 2*t^3*(1 - 2*t^2)/(1 - t^4)^2)/(1 - 2*t^2)
Abrimos la expresión [src] 
     ________          /            3            \
    /   1     /     4\ | -2*t    2*t *(1 - 2*t*t)|
   /  ------ *\1 - t /*|------ + ----------------|
  /        4           |     4              2    |
\/    1 - t            |1 - t       /     4\     |
                       \            \1 - t /     /
--------------------------------------------------
                    ___________                   
                  \/ 1 - 2*t*t
$$\frac{\left(1 - t^{4}\right) \left(\frac{\left(-1\right) 2 t}{1 - t^{4}} + \frac{2 t^{3} \left(- t 2 t + 1\right)}{\left(1 - t^{4}\right)^{2}}\right) \sqrt{\frac{1}{1 - t^{4}}}}{\sqrt{- t 2 t + 1}}$$ 
sqrt(1/(1 - t^4))*(1 - t^4)*((-2*t)/(1 - t^4) + ((2*t^3)*(1 - 2*t*t))/(1 - t^4)^2)/sqrt(1 - 2*t*t)
Potencias [src] 
      __________                                      
     /        2           /              3 /       2\\
    /  1 - 2*t   /     4\ |   2*t     2*t *\1 - 2*t /|
   /   -------- *\1 - t /*|- ------ + ---------------|
  /          4            |       4              2   |
\/      1 - t             |  1 - t       /     4\    |
                          \              \1 - t /    /
------------------------------------------------------
                              2                       
                       1 - 2*t
$$\frac{\sqrt{\frac{1 - 2 t^{2}}{1 - t^{4}}} \left(1 - t^{4}\right) \left(\frac{2 t^{3} \left(1 - 2 t^{2}\right)}{\left(1 - t^{4}\right)^{2}} - \frac{2 t}{1 - t^{4}}\right)}{1 - 2 t^{2}}$$ 
      __________                                    
     /        2           /            3 /       2\\
    /  1 - 2*t   /     4\ |   2*t     t *\2 - 4*t /|
   /   -------- *\1 - t /*|- ------ + -------------|
  /          4            |       4             2  |
\/      1 - t             |  1 - t      /     4\   |
                          \             \1 - t /   /
----------------------------------------------------
                             2                      
                      1 - 2*t
$$\frac{\sqrt{\frac{1 - 2 t^{2}}{1 - t^{4}}} \left(1 - t^{4}\right) \left(\frac{t^{3} \left(2 - 4 t^{2}\right)}{\left(1 - t^{4}\right)^{2}} - \frac{2 t}{1 - t^{4}}\right)}{1 - 2 t^{2}}$$ 
sqrt((1 - 2*t^2)/(1 - t^4))*(1 - t^4)*(-2*t/(1 - t^4) + t^3*(2 - 4*t^2)/(1 - t^4)^2)/(1 - 2*t^2)
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