Descomposición de una fracción sqrt((x+2)/(x-2))+sqrt((x-2)/(x+2))/sqrt((x+2)/(x-2))-sqrt((x-2)/(x+2)) (raíz cuadrada de ((x más 2) dividir por (x menos 2)) más raíz cuadrada de ((x menos 2) dividir por (x más 2)) dividir por raíz cuadrada de ((x más 2) dividir por (x menos 2)) menos raíz cuadrada de ((x menos 2) dividir por (x más 2)))

Ha introducido [src]

                  _______              
                 / x - 2               
    _______     /  -----        _______
   / x + 2    \/   x + 2       / x - 2 
  /  -----  + ----------- -   /  ----- 
\/   x - 2        _______   \/   x + 2 
                 / x + 2               
                /  -----               
              \/   x - 2

- \sqrt{\frac{x - 2}{x + 2}} + \left(\sqrt{\frac{x + 2}{x - 2}} + \frac{\sqrt{\frac{x - 2}{x + 2}}}{\sqrt{\frac{x + 2}{x - 2}}}\right)

sqrt((x + 2)/(x - 2)) + sqrt((x - 2)/(x + 2))/sqrt((x + 2)/(x - 2)) - sqrt((x - 2)/(x + 2))

Simplificación general [src]

    ________       ________ /    ________       ________\
   / -2 + x       / 2 + x   |   / 2 + x        / -2 + x |
  /  ------  +   /  ------ *|  /  ------  -   /  ------ |
\/   2 + x     \/   -2 + x  \\/   -2 + x    \/   2 + x  /
---------------------------------------------------------
                           ________                      
                          / 2 + x                        
                         /  ------                       
                       \/   -2 + x

\frac{\sqrt{\frac{x + 2}{x - 2}} \left(\sqrt{\frac{x + 2}{x - 2}} - \sqrt{\frac{x - 2}{x + 2}}\right) + \sqrt{\frac{x - 2}{x + 2}}}{\sqrt{\frac{x + 2}{x - 2}}}

(sqrt((-2 + x)/(2 + x)) + sqrt((2 + x)/(-2 + x))*(sqrt((2 + x)/(-2 + x)) - sqrt((-2 + x)/(2 + x))))/sqrt((2 + x)/(-2 + x))

Respuesta numérica [src]

((2.0 + x)/(-2.0 + x))^0.5 - ((-2.0 + x)/(2.0 + x))^0.5 + ((-2.0 + x)/(2.0 + x))^0.5*((2.0 + x)/(-2.0 + x))^(-0.5)

((2.0 + x)/(-2.0 + x))^0.5 - ((-2.0 + x)/(2.0 + x))^0.5 + ((-2.0 + x)/(2.0 + x))^0.5*((2.0 + x)/(-2.0 + x))^(-0.5)

Unión de expresiones racionales [src]

    ________                ________     ________
   / -2 + x    2 + x       / 2 + x      / -2 + x 
  /  ------  + ------ -   /  ------ *  /  ------ 
\/   2 + x     -2 + x   \/   -2 + x  \/   2 + x  
-------------------------------------------------
                       ________                  
                      / 2 + x                    
                     /  ------                   
                   \/   -2 + x

\frac{- \sqrt{\frac{x + 2}{x - 2}} \sqrt{\frac{x - 2}{x + 2}} + \sqrt{\frac{x - 2}{x + 2}} + \frac{x + 2}{x - 2}}{\sqrt{\frac{x + 2}{x - 2}}}

(sqrt((-2 + x)/(2 + x)) + (2 + x)/(-2 + x) - sqrt((2 + x)/(-2 + x))*sqrt((-2 + x)/(2 + x)))/sqrt((2 + x)/(-2 + x))

Denominador común [src]

 /               _________________         _________________         _________________     _________________         _________________     _________________\ 
 |              /     2       x           /     2       x           /     2       x       /   2        x            /     2       x       /   2        x    | 
-|-2 - x + 2*  /  - ----- + -----  - x*  /  - ----- + -----  - 2*  /  - ----- + ----- *  /  ------ + ------  + x*  /  - ----- + ----- *  /  ------ + ------ | 
 \           \/     2 + x   2 + x      \/     2 + x   2 + x      \/     2 + x   2 + x  \/   -2 + x   -2 + x      \/     2 + x   2 + x  \/   -2 + x   -2 + x / 
--------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                             _________________         _________________                                                      
                                                            /   2        x            /   2        x                                                          
                                                     - 2*  /  ------ + ------  + x*  /  ------ + ------                                                       
                                                         \/   -2 + x   -2 + x      \/   -2 + x   -2 + x

- \frac{x \sqrt{\frac{x}{x - 2} + \frac{2}{x - 2}} \sqrt{\frac{x}{x + 2} - \frac{2}{x + 2}} - x \sqrt{\frac{x}{x + 2} - \frac{2}{x + 2}} - x - 2 \sqrt{\frac{x}{x - 2} + \frac{2}{x - 2}} \sqrt{\frac{x}{x + 2} - \frac{2}{x + 2}} + 2 \sqrt{\frac{x}{x + 2} - \frac{2}{x + 2}} - 2}{x \sqrt{\frac{x}{x - 2} + \frac{2}{x - 2}} - 2 \sqrt{\frac{x}{x - 2} + \frac{2}{x - 2}}}

-(-2 - x + 2*sqrt(-2/(2 + x) + x/(2 + x)) - x*sqrt(-2/(2 + x) + x/(2 + x)) - 2*sqrt(-2/(2 + x) + x/(2 + x))*sqrt(2/(-2 + x) + x/(-2 + x)) + x*sqrt(-2/(2 + x) + x/(2 + x))*sqrt(2/(-2 + x) + x/(-2 + x)))/(-2*sqrt(2/(-2 + x) + x/(-2 + x)) + x*sqrt(2/(-2 + x) + x/(-2 + x)))

Combinatoria [src]

    _________________                         _________________     _________________
   /     2       x        2        x         /     2       x       /   2        x    
  /  - ----- + -----  + ------ + ------ -   /  - ----- + ----- *  /  ------ + ------ 
\/     2 + x   2 + x    -2 + x   -2 + x   \/     2 + x   2 + x  \/   -2 + x   -2 + x 
-------------------------------------------------------------------------------------
                                         ________                                    
                                        / 2 + x                                      
                                       /  ------                                     
                                     \/   -2 + x

\frac{\frac{x}{x - 2} - \sqrt{\frac{x}{x - 2} + \frac{2}{x - 2}} \sqrt{\frac{x}{x + 2} - \frac{2}{x + 2}} + \sqrt{\frac{x}{x + 2} - \frac{2}{x + 2}} + \frac{2}{x - 2}}{\sqrt{\frac{x + 2}{x - 2}}}

(sqrt(-2/(2 + x) + x/(2 + x)) + 2/(-2 + x) + x/(-2 + x) - sqrt(-2/(2 + x) + x/(2 + x))*sqrt(2/(-2 + x) + x/(-2 + x)))/sqrt((2 + x)/(-2 + x))

Denominador racional [src]

    _________________                       _________________     _______________
   /     2       x        2       x        /     2       x       /   2       x   
  /  - ----- + -----  + ----- + ----- -   /  - ----- + ----- *  /  ----- + ----- 
\/     x + 2   x + 2    x - 2   x - 2   \/     x + 2   x + 2  \/   x - 2   x - 2 
---------------------------------------------------------------------------------
                                  _________________                              
                                 /   2        x                                  
                                /  ------ + ------                               
                              \/   -2 + x   -2 + x

\frac{\frac{x}{x - 2} - \sqrt{\frac{x}{x - 2} + \frac{2}{x - 2}} \sqrt{\frac{x}{x + 2} - \frac{2}{x + 2}} + \sqrt{\frac{x}{x + 2} - \frac{2}{x + 2}} + \frac{2}{x - 2}}{\sqrt{\frac{x}{x - 2} + \frac{2}{x - 2}}}

(sqrt(-2/(x + 2) + x/(x + 2)) + 2/(x - 2) + x/(x - 2) - sqrt(-2/(x + 2) + x/(x + 2))*sqrt(2/(x - 2) + x/(x - 2)))/sqrt(2/(-2 + x) + x/(-2 + x))

Abrimos la expresión [src]

                                _______
                               / x - 2 
    _______       _______     /  ----- 
   / x + 2       / x - 2    \/   x + 2 
  /  -----  -   /  -----  + -----------
\/   x - 2    \/   x + 2        _______
                               / x + 2 
                              /  ----- 
                            \/   x - 2

\sqrt{\frac{x + 2}{x - 2}} - \sqrt{\frac{x - 2}{x + 2}} + \frac{\sqrt{\frac{x - 2}{x + 2}}}{\sqrt{\frac{x + 2}{x - 2}}}

                                                    _______          
                                                   /   1      _______
    _______                 _______               /  ----- *\/ x - 2 
   /   1      _______      /   1      _______   \/   x + 2           
  /  ----- *\/ x + 2  -   /  ----- *\/ x - 2  + ---------------------
\/   x - 2              \/   x + 2                  _______          
                                                   /   1      _______
                                                  /  ----- *\/ x + 2 
                                                \/   x - 2

- \sqrt{x - 2} \sqrt{\frac{1}{x + 2}} + \frac{\sqrt{x - 2} \sqrt{\frac{1}{x + 2}}}{\sqrt{x + 2} \sqrt{\frac{1}{x - 2}}} + \sqrt{x + 2} \sqrt{\frac{1}{x - 2}}

sqrt(1/(x - 2))*sqrt(x + 2) - sqrt(1/(x + 2))*sqrt(x - 2) + sqrt(1/(x + 2))*sqrt(x - 2)/(sqrt(1/(x - 2))*sqrt(x + 2))

Compilar la expresión [src]

                                  ________
                                 / -2 + x 
    ________       ________     /  ------ 
   / 2 + x        / -2 + x    \/   2 + x  
  /  ------  -   /  ------  + ------------
\/   -2 + x    \/   2 + x         ________
                                 / 2 + x  
                                /  ------ 
                              \/   -2 + x

\sqrt{\frac{x + 2}{x - 2}} - \sqrt{\frac{x - 2}{x + 2}} + \frac{\sqrt{\frac{x - 2}{x + 2}}}{\sqrt{\frac{x + 2}{x - 2}}}

sqrt((2 + x)/(-2 + x)) - sqrt((-2 + x)/(2 + x)) + sqrt((-2 + x)/(2 + x))/sqrt((2 + x)/(-2 + x))

Parte trigonométrica [src]

                                  ________
                                 / -2 + x 
    ________       ________     /  ------ 
   / 2 + x        / -2 + x    \/   2 + x  
  /  ------  -   /  ------  + ------------
\/   -2 + x    \/   2 + x         ________
                                 / 2 + x  
                                /  ------ 
                              \/   -2 + x

\sqrt{\frac{x + 2}{x - 2}} - \sqrt{\frac{x - 2}{x + 2}} + \frac{\sqrt{\frac{x - 2}{x + 2}}}{\sqrt{\frac{x + 2}{x - 2}}}

sqrt((2 + x)/(-2 + x)) - sqrt((-2 + x)/(2 + x)) + sqrt((-2 + x)/(2 + x))/sqrt((2 + x)/(-2 + x))

Potencias [src]

                                  ________
                                 / -2 + x 
    ________       ________     /  ------ 
   / 2 + x        / -2 + x    \/   2 + x  
  /  ------  -   /  ------  + ------------
\/   -2 + x    \/   2 + x         ________
                                 / 2 + x  
                                /  ------ 
                              \/   -2 + x

\sqrt{\frac{x + 2}{x - 2}} - \sqrt{\frac{x - 2}{x + 2}} + \frac{\sqrt{\frac{x - 2}{x + 2}}}{\sqrt{\frac{x + 2}{x - 2}}}

sqrt((2 + x)/(-2 + x)) - sqrt((-2 + x)/(2 + x)) + sqrt((-2 + x)/(2 + x))/sqrt((2 + x)/(-2 + x))

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