Descomposición de una fracción sqrt((x+1)/(x-1))*(x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)²))/(x+1) (raíz cuadrada de ((x más 1) dividir por (x menos 1)) multiplicar por (x menos 1) multiplicar por (1 dividir por (2 multiplicar por (x menos 1)) menos (x más 1) dividir por (2 multiplicar por (x menos 1) al cuadrado)) dividir por (x más 1))

Ha introducido [src]

    _______                                 
   / x + 1          /    1         x + 1   \
  /  ----- *(x - 1)*|--------- - ----------|
\/   x - 1          |2*(x - 1)            2|
                    \            2*(x - 1) /
--------------------------------------------
                   x + 1

\frac{\sqrt{\frac{x + 1}{x - 1}} \left(x - 1\right) \left(- \frac{x + 1}{2 \left(x - 1\right)^{2}} + \frac{1}{2 \left(x - 1\right)}\right)}{x + 1}

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

Simplificación general [src]

     ________ 
    / 1 + x   
-  /  ------  
 \/   -1 + x  
--------------
         2    
   -1 + x

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

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

Respuesta numérica [src]

((1.0 + x)/(-1.0 + x))^0.5*(-1.0 + x)*(1/(-2.0 + 2.0*x) - 0.5*(1.0 + x)/(-1.0 + x)^2)/(1.0 + x)

((1.0 + x)/(-1.0 + x))^0.5*(-1.0 + x)*(1/(-2.0 + 2.0*x) - 0.5*(1.0 + x)/(-1.0 + x)^2)/(1.0 + x)

Denominador racional [src]

      _______________            _______________                   _______________
     /   1       x         2    /   1       x                2    /   1       x   
2*  /  ----- + -----  - 2*x *  /  ----- + -----  + 2*(-1 + x) *  /  ----- + ----- 
  \/   x - 1   x - 1         \/   x - 1   x - 1                \/   x - 1   x - 1 
----------------------------------------------------------------------------------
                          2*(1 + x)*(-1 + x)*(-2 + 2*x)

\frac{- 2 x^{2} \sqrt{\frac{x}{x - 1} + \frac{1}{x - 1}} + 2 \left(x - 1\right)^{2} \sqrt{\frac{x}{x - 1} + \frac{1}{x - 1}} + 2 \sqrt{\frac{x}{x - 1} + \frac{1}{x - 1}}}{2 \left(x - 1\right) \left(x + 1\right) \left(2 x - 2\right)}

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

Parte trigonométrica [src]

    ________                                  
   / 1 + x            /   1          1 + x   \
  /  ------ *(-1 + x)*|-------- - -----------|
\/   -1 + x           |-2 + 2*x             2|
                      \           2*(-1 + x) /
----------------------------------------------
                    1 + x

\frac{\sqrt{\frac{x + 1}{x - 1}} \left(x - 1\right) \left(\frac{1}{2 x - 2} - \frac{x + 1}{2 \left(x - 1\right)^{2}}\right)}{x + 1}

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

Combinatoria [src]

      ________  
     / 1 + x    
 -  /  ------   
  \/   -1 + x   
----------------
(1 + x)*(-1 + x)

- \frac{\sqrt{\frac{x + 1}{x - 1}}}{\left(x - 1\right) \left(x + 1\right)}

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

Unión de expresiones racionales [src]

      ________  
     / 1 + x    
 -  /  ------   
  \/   -1 + x   
----------------
(1 + x)*(-1 + x)

- \frac{\sqrt{\frac{x + 1}{x - 1}}}{\left(x - 1\right) \left(x + 1\right)}

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

Abrimos la expresión [src]

    _______                                 
   /   1            /    1         x + 1   \
  /  ----- *(x - 1)*|--------- - ----------|
\/   x - 1          |2*(x - 1)            2|
                    \            2*(x - 1) /
--------------------------------------------
                   _______                  
                 \/ x + 1

\frac{\left(x - 1\right) \left(\frac{1}{2 \left(x - 1\right)} - \frac{x + 1}{2 \left(x - 1\right)^{2}}\right) \sqrt{\frac{1}{x - 1}}}{\sqrt{x + 1}}

    _______                                 
   / x + 1          /    1         x + 1   \
  /  ----- *(x - 1)*|--------- - ----------|
\/   x - 1          |2*(x - 1)            2|
                    \            2*(x - 1) /
--------------------------------------------
                   x + 1

\frac{\sqrt{\frac{x + 1}{x - 1}} \left(x - 1\right) \left(\frac{1}{2 \left(x - 1\right)} - \frac{x + 1}{2 \left(x - 1\right)^{2}}\right)}{x + 1}

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

Compilar la expresión [src]

    ________                                  
   / 1 + x            /   1          1 + x   \
  /  ------ *(-1 + x)*|-------- - -----------|
\/   -1 + x           |-2 + 2*x             2|
                      \           2*(-1 + x) /
----------------------------------------------
                    1 + x

\frac{\sqrt{\frac{x + 1}{x - 1}} \left(x - 1\right) \left(\frac{1}{2 x - 2} - \frac{x + 1}{2 \left(x - 1\right)^{2}}\right)}{x + 1}

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

Potencias [src]

    ________                                  
   / 1 + x            /   1          1 + x   \
  /  ------ *(-1 + x)*|-------- - -----------|
\/   -1 + x           |-2 + 2*x             2|
                      \           2*(-1 + x) /
----------------------------------------------
                    1 + x

\frac{\sqrt{\frac{x + 1}{x - 1}} \left(x - 1\right) \left(\frac{1}{2 x - 2} - \frac{x + 1}{2 \left(x - 1\right)^{2}}\right)}{x + 1}

                      /              1   x \
    ________          |            - - - - |
   / 1 + x            |   1          2   2 |
  /  ------ *(-1 + x)*|-------- + ---------|
\/   -1 + x           |-2 + 2*x           2|
                      \           (-1 + x) /
--------------------------------------------
                   1 + x

\frac{\sqrt{\frac{x + 1}{x - 1}} \left(x - 1\right) \left(\frac{- \frac{x}{2} - \frac{1}{2}}{\left(x - 1\right)^{2}} + \frac{1}{2 x - 2}\right)}{x + 1}

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

Denominador común [src]

     _________________ 
    /   1        x     
-  /  ------ + ------  
 \/   -1 + x   -1 + x  
-----------------------
              2        
        -1 + x

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

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

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