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

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Вы ввели [src]
                 /          x - 1\ / x - 1    2    \
  x - 1          |-log(x) - -----|*\E      + x  - 2/
 E      + 2*x    \            x  /                  
-------------- + -----------------------------------
(x - 1)*log(x)                    2    2            
                           (x - 1) *log (x)
$$\frac{1}{\left(x - 1\right)^{2} \log^{2}{\left (x \right )}} \left(e^{x - 1} + x^{2} - 2\right) \left(- \log{\left (x \right )} - \frac{1}{x} \left(x - 1\right)\right) + \frac{e^{x - 1} + 2 x}{\left(x - 1\right) \log{\left (x \right )}}$$
Степени [src]
                  /          1 - x\ /      2    -1 + x\
        -1 + x    |-log(x) + -----|*\-2 + x  + e      /
 2*x + e          \            x  /                    
--------------- + -------------------------------------
(-1 + x)*log(x)                     2    2             
                            (-1 + x) *log (x)
$$\frac{2 x + e^{x - 1}}{\left(x - 1\right) \log{\left (x \right )}} + \frac{1}{\left(x - 1\right)^{2} \log^{2}{\left (x \right )}} \left(- \log{\left (x \right )} + \frac{1}{x} \left(- x + 1\right)\right) \left(x^{2} + e^{x - 1} - 2\right)$$
                  /          -1 + x\ /      2    -1 + x\
        -1 + x    |-log(x) - ------|*\-2 + x  + e      /
 2*x + e          \            x   /                    
--------------- + --------------------------------------
(-1 + x)*log(x)                     2    2              
                            (-1 + x) *log (x)
$$\frac{2 x + e^{x - 1}}{\left(x - 1\right) \log{\left (x \right )}} + \frac{1}{\left(x - 1\right)^{2} \log^{2}{\left (x \right )}} \left(- \log{\left (x \right )} - \frac{1}{x} \left(x - 1\right)\right) \left(x^{2} + e^{x - 1} - 2\right)$$
Численный ответ [src]
(2.71828182845905^(-1.0 + x) + 2.0*x)/((-1.0 + x)*log(x)) + (-log(x) - (-1.0 + x)/x)*(-2.0 + 2.71828182845905^(-1.0 + x) + x^2)/((-1.0 + x)^2*log(x)^2)
Рациональный знаменатель [src]
            2           3    2       4    2       4           -1 + x                              2         2    2         3               2     -1 + x    2    2     -1 + x    2  -1 + x               -1 + x             2         2    2                2    2     -1 + x
2*log(x) + x *log(x) + x *log (x) - x *log (x) - x *log(x) - e      *log(x) - 4*x*log(x) - 2*x*log (x) + 2*x *log (x) + 2*x *log(x) + x*log (x)*e       - x *log (x)*e       - x *e      *log(x) + 2*x*e      *log(x) + 2*x *(-1 + x) *log (x) + x*(-1 + x) *log (x)*e      
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                      3    3                                                                                                                                
                                                                                                                            x*(-1 + x) *log (x)
$$\frac{1}{x \left(x - 1\right)^{3} \log^{3}{\left (x \right )}} \left(- x^{4} \log^{2}{\left (x \right )} - x^{4} \log{\left (x \right )} + x^{3} \log^{2}{\left (x \right )} + 2 x^{3} \log{\left (x \right )} + 2 x^{2} \left(x - 1\right)^{2} \log^{2}{\left (x \right )} - x^{2} e^{x - 1} \log^{2}{\left (x \right )} - x^{2} e^{x - 1} \log{\left (x \right )} + 2 x^{2} \log^{2}{\left (x \right )} + x^{2} \log{\left (x \right )} + x \left(x - 1\right)^{2} e^{x - 1} \log^{2}{\left (x \right )} + x e^{x - 1} \log^{2}{\left (x \right )} + 2 x e^{x - 1} \log{\left (x \right )} - 2 x \log^{2}{\left (x \right )} - 4 x \log{\left (x \right )} - e^{x - 1} \log{\left (x \right )} + 2 \log{\left (x \right )}\right)$$
Объединение рациональных выражений [src]
                   /      2    -1 + x\              /       -1 + x\       
(1 - x - x*log(x))*\-2 + x  + e      / + x*(-1 + x)*\2*x + e      /*log(x)
--------------------------------------------------------------------------
                                     2    2                               
                           x*(-1 + x) *log (x)
$$\frac{1}{x \left(x - 1\right)^{2} \log^{2}{\left (x \right )}} \left(x \left(x - 1\right) \left(2 x + e^{x - 1}\right) \log{\left (x \right )} + \left(x^{2} + e^{x - 1} - 2\right) \left(- x \log{\left (x \right )} - x + 1\right)\right)$$
Общее упрощение [src]
                      /      2    -1 + x\              /       -1 + x\       
- (-1 + x + x*log(x))*\-2 + x  + e      / + x*(-1 + x)*\2*x + e      /*log(x)
-----------------------------------------------------------------------------
                                       2    2                                
                             x*(-1 + x) *log (x)
$$\frac{1}{x \left(x - 1\right)^{2} \log^{2}{\left (x \right )}} \left(x \left(x - 1\right) \left(2 x + e^{x - 1}\right) \log{\left (x \right )} - \left(x^{2} + e^{x - 1} - 2\right) \left(x \log{\left (x \right )} + x - 1\right)\right)$$
Собрать выражение [src]
         /  /       / 2\\   /        / 2\\  x\    2 /  /       / 2\\    x       \      3                  x
-2*E + x*\E*\2 + log\x // + \-1 - log\x //*e / + x *\E*\1 - log\x // + e *log(x)/ + E*x *(-1 + log(x)) + e 
-----------------------------------------------------------------------------------------------------------
                                       2         3    2           2    2                                   
                                E*x*log (x) + E*x *log (x) - 2*E*x *log (x)
$$\frac{1}{e x^{3} \log^{2}{\left (x \right )} - 2 e x^{2} \log^{2}{\left (x \right )} + e x \log^{2}{\left (x \right )}} \left(e x^{3} \left(\log{\left (x \right )} - 1\right) + x^{2} \left(e \left(- \log{\left (x^{2} \right )} + 1\right) + e^{x} \log{\left (x \right )}\right) + x \left(\left(- \log{\left (x^{2} \right )} - 1\right) e^{x} + e \left(\log{\left (x^{2} \right )} + 2\right)\right) + e^{x} - 2 e\right)$$
Общий знаменатель [src]
          2      3      x              3           2  x               2               x                          x
-2*E + E*x  - E*x  - x*e  + 2*E*x + E*x *log(x) + x *e *log(x) - 2*E*x *log(x) - 2*x*e *log(x) + 2*E*x*log(x) + e 
------------------------------------------------------------------------------------------------------------------
                                          2         3    2           2    2                                       
                                   E*x*log (x) + E*x *log (x) - 2*E*x *log (x)
$$\frac{1}{e x^{3} \log^{2}{\left (x \right )} - 2 e x^{2} \log^{2}{\left (x \right )} + e x \log^{2}{\left (x \right )}} \left(e x^{3} \log{\left (x \right )} - e x^{3} + x^{2} e^{x} \log{\left (x \right )} - 2 e x^{2} \log{\left (x \right )} + e x^{2} - 2 x e^{x} \log{\left (x \right )} - x e^{x} + 2 e x \log{\left (x \right )} + 2 e x + e^{x} - 2 e\right)$$
Комбинаторика [src]
      2    3          3           -1  x      2                          -1  x    2  -1  x               -1  x       
-2 + x  - x  + 2*x + x *log(x) + e  *e  - 2*x *log(x) + 2*x*log(x) - x*e  *e  + x *e  *e *log(x) - 2*x*e  *e *log(x)
--------------------------------------------------------------------------------------------------------------------
                                                          2    2                                                    
                                                x*(-1 + x) *log (x)
$$\frac{1}{x \left(x - 1\right)^{2} \log^{2}{\left (x \right )}} \left(x^{3} \log{\left (x \right )} - x^{3} + \frac{x^{2} e^{x}}{e} \log{\left (x \right )} - 2 x^{2} \log{\left (x \right )} + x^{2} - \frac{2 x}{e} e^{x} \log{\left (x \right )} - \frac{x e^{x}}{e} + 2 x \log{\left (x \right )} + 2 x + \frac{e^{x}}{e} - 2\right)$$
Раскрыть выражение [src]
                 /          x - 1\ / x - 1    2    \
  x - 1          |-log(x) - -----|*\E      + x  - 2/
 E      + 2*x    \            x  /                  
-------------- + -----------------------------------
(x - 1)*log(x)                    2    2            
                           (x - 1) *log (x)
$$\frac{e^{x - 1} + 2 x}{\left(x - 1\right) \log{\left (x \right )}} + \frac{1}{\left(x - 1\right)^{2} \log^{2}{\left (x \right )}} \left(e^{x - 1} + x^{2} - 2\right) \left(- \log{\left (x \right )} - \frac{1}{x} \left(x - 1\right)\right)$$
                  /          -1 + x\ /      2    -1 + x\
        -1 + x    |-log(x) - ------|*\-2 + x  + e      /
 2*x + e          \            x   /                    
--------------- + --------------------------------------
(-1 + x)*log(x)                     2    2              
                            (-1 + x) *log (x)
$$\frac{2 x + e^{x - 1}}{\left(x - 1\right) \log{\left (x \right )}} + \frac{1}{\left(x - 1\right)^{2} \log^{2}{\left (x \right )}} \left(- \log{\left (x \right )} - \frac{1}{x} \left(x - 1\right)\right) \left(x^{2} + e^{x - 1} - 2\right)$$