Калькуляторы онлайн/ Решение уравнений/ Упрощение выражений/ Общий знаменатель/ (x-1)^(1/log(2*(x-1)))*(1/((x-1)*log(2*(x-1)))-log(x-1)/((x-1)*log(2*(x-1))^2))

Общий знаменатель (x-1)^(1/log(2*(x-1)))*(1 ... )/((x-1)*log(2*(x-1))^2))

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Примеры

Решение

Вы ввели [src]
             1                                                          
       --------------                                                   
       log(2*(x - 1)) /          1                     log(x - 1)      \
(x - 1)              *|---------------------- - -----------------------|
                      |(x - 1)*log(2*(x - 1))              2           |
                      \                         (x - 1)*log (2*(x - 1))/
$$\left(x - 1\right)^{\frac{1}{\log{\left (2 \left(x - 1\right) \right )}}} \left(- \frac{1}{\left(x - 1\right) \log^{2}{\left (2 \left(x - 1\right) \right )}} \log{\left (x - 1 \right )} + \frac{1}{\left(x - 1\right) \log{\left (2 \left(x - 1\right) \right )}}\right)$$
Степени [src]
              1                                                         
        -------------                                                   
        log(-2 + 2*x) /          1                    log(-1 + x)      \
(-1 + x)             *|---------------------- - -----------------------|
                      |(-1 + x)*log(-2 + 2*x)               2          |
                      \                         (-1 + x)*log (-2 + 2*x)/
$$\left(x - 1\right)^{\frac{1}{\log{\left (2 x - 2 \right )}}} \left(- \frac{\log{\left (x - 1 \right )}}{\left(x - 1\right) \log^{2}{\left (2 x - 2 \right )}} + \frac{1}{\left(x - 1\right) \log{\left (2 x - 2 \right )}}\right)$$
Численный ответ [src]
(-1.0 + x)^(1/log(2*(x - 1)))*(1/((-1.0 + x)*log(2*(x - 1))) - log(x - 1)/((-1.0 + x)*log(2*(x - 1))^2))
Рациональный знаменатель [src]
                     1                                             1                                           1                                                        1                                
          -2 + -------------                            -2 + -------------                          -2 + -------------                                       -2 + -------------                          
               log(-2 + 2*x)    2                            log(-2 + 2*x)    2                          log(-2 + 2*x)                                            log(-2 + 2*x)                          
- (-1 + x)                  *log (-2 + 2*x) + x*(-1 + x)                  *log (-2 + 2*x) + (-1 + x)                  *log(-1 + x)*log(-2 + 2*x) - x*(-1 + x)                  *log(-1 + x)*log(-2 + 2*x)
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 3                                                                                                       
                                                                                              log (-2 + 2*x)
$$\frac{1}{\log^{3}{\left (2 x - 2 \right )}} \left(- x \left(x - 1\right)^{-2 + \frac{1}{\log{\left (2 x - 2 \right )}}} \log{\left (x - 1 \right )} \log{\left (2 x - 2 \right )} + x \left(x - 1\right)^{-2 + \frac{1}{\log{\left (2 x - 2 \right )}}} \log^{2}{\left (2 x - 2 \right )} + \left(x - 1\right)^{-2 + \frac{1}{\log{\left (2 x - 2 \right )}}} \log{\left (x - 1 \right )} \log{\left (2 x - 2 \right )} - \left(x - 1\right)^{-2 + \frac{1}{\log{\left (2 x - 2 \right )}}} \log^{2}{\left (2 x - 2 \right )}\right)$$
Объединение рациональных выражений [src]
              1                                     
        -------------                               
        log(-2 + 2*x)                               
(-1 + x)             *(-log(-1 + x) + log(-2 + 2*x))
----------------------------------------------------
                          2                         
              (-1 + x)*log (-2 + 2*x)
$$\frac{\left(x - 1\right)^{\frac{1}{\log{\left (2 x - 2 \right )}}}}{\left(x - 1\right) \log^{2}{\left (2 x - 2 \right )}} \left(- \log{\left (x - 1 \right )} + \log{\left (2 x - 2 \right )}\right)$$
Общее упрощение [src]
            1 - 2*log(2) - 2*log(-1 + x)       
        1 + ----------------------------       
                log(2) + log(-1 + x)           
(-1 + x)                                *log(2)
-----------------------------------------------
                                  2            
            (log(2) + log(-1 + x))
$$\frac{\log{\left (2 \right )}}{\left(\log{\left (x - 1 \right )} + \log{\left (2 \right )}\right)^{2}} \left(x - 1\right)^{1 + \frac{- 2 \log{\left (x - 1 \right )} - 2 \log{\left (2 \right )} + 1}{\log{\left (x - 1 \right )} + \log{\left (2 \right )}}}$$
Собрать выражение [src]
               1                                         
         -------------                                   
         log(-2 + 2*x) /        3                      \ 
-(-1 + x)             *\-1 + log (-2 + 2*x)*log(-1 + x)/ 
---------------------------------------------------------
             -log(-2 + 2*x) + x*log(-2 + 2*x)
$$- \frac{\left(x - 1\right)^{\frac{1}{\log{\left (2 x - 2 \right )}}} \left(\log{\left (x - 1 \right )} \log^{3}{\left (2 x - 2 \right )} - 1\right)}{x \log{\left (2 x - 2 \right )} - \log{\left (2 x - 2 \right )}}$$
              1                                                          
        --------------                                                   
        log(2*(x - 1)) /          1                     log(x - 1)      \
(-1 + x)              *|---------------------- - -----------------------|
                       |(x - 1)*log(2*(x - 1))              2           |
                       \                         (x - 1)*log (2*(x - 1))/
$$\left(x - 1\right)^{\frac{1}{\log{\left (2 \left(x - 1\right) \right )}}} \left(\frac{1}{\left(x - 1\right) \log{\left (2 \left(x - 1\right) \right )}} - \frac{1}{\left(x - 1\right) \log^{2}{\left (2 \left(x - 1\right) \right )}} \log{\left (x - 1 \right )}\right)$$
Комбинаторика [src]
              1                                     
        -------------                               
        log(-2 + 2*x)                               
(-1 + x)             *(-log(-1 + x) + log(-2 + 2*x))
----------------------------------------------------
                          2                         
              (-1 + x)*log (-2 + 2*x)
$$\frac{\left(x - 1\right)^{\frac{1}{\log{\left (2 x - 2 \right )}}}}{\left(x - 1\right) \log^{2}{\left (2 x - 2 \right )}} \left(- \log{\left (x - 1 \right )} + \log{\left (2 x - 2 \right )}\right)$$
Общий знаменатель [src]
                                                  1                                                  
                                         --------------------                                        
                                         log(2) + log(-1 + x)                                        
                                 (-1 + x)                    *log(2)                                 
-----------------------------------------------------------------------------------------------------
     2         2                2           2                                                        
- log (2) - log (-1 + x) + x*log (2) + x*log (-1 + x) - 2*log(2)*log(-1 + x) + 2*x*log(2)*log(-1 + x)
$$\frac{\left(x - 1\right)^{\frac{1}{\log{\left (x - 1 \right )} + \log{\left (2 \right )}}} \log{\left (2 \right )}}{x \log^{2}{\left (x - 1 \right )} + 2 x \log{\left (2 \right )} \log{\left (x - 1 \right )} + x \log^{2}{\left (2 \right )} - \log^{2}{\left (x - 1 \right )} - 2 \log{\left (2 \right )} \log{\left (x - 1 \right )} - \log^{2}{\left (2 \right )}}$$
Раскрыть выражение [src]
             1                                                          
       --------------                                                   
       log(2*(x - 1)) /          1                     log(x - 1)      \
(x - 1)              *|---------------------- - -----------------------|
                      |(x - 1)*log(2*(x - 1))              2           |
                      \                         (x - 1)*log (2*(x - 1))/
$$\left(x - 1\right)^{\frac{1}{\log{\left (2 \left(x - 1\right) \right )}}} \left(- \frac{\log{\left (x - 1 \right )}}{\left(x - 1\right) \log^{2}{\left (2 \left(x - 1\right) \right )}} + \frac{1}{\left(x - 1\right) \log{\left (2 \left(x - 1\right) \right )}}\right)$$
                 1                                                                                  
        -------------------- /                                                        2            \
        log(2) + log(-1 + x) |               1                  (log(2) + log(-1 + x)) *log(-1 + x)|
(-1 + x)                    *|------------------------------- - -----------------------------------|
                             \(-1 + x)*(log(2) + log(-1 + x))                  -1 + x              /
$$\left(x - 1\right)^{\frac{1}{\log{\left (x - 1 \right )} + \log{\left (2 \right )}}} \left(- \frac{\log{\left (x - 1 \right )}}{x - 1} \left(\log{\left (x - 1 \right )} + \log{\left (2 \right )}\right)^{2} + \frac{1}{\left(x - 1\right) \left(\log{\left (x - 1 \right )} + \log{\left (2 \right )}\right)}\right)$$