Общий знаменатель -1/3*x^(1/3)*(x+2)^2+(4-x ... 2*x))/(9*x^(2/3)*(x+2)^4)

Вы ввели

                           /         /   2/3\                    \
                           |         |/2\   |                    |
                           |         ||-|   |                    |
 3 ___                     |         \\x/   /     3 ___          |
-\/ x          2   (4 - x)*\- (x + 2)         - 3*\/ x *(4 + 2*x)/
-------*(x + 2)  + -----------------------------------------------
   3                                  2/3        4                
                                   9*x   *(x + 2)                 

$$- \frac{\sqrt[3]{x}}{3} \left(x + 2\right)^{2} + \frac{1}{9 x^{\frac{2}{3}} \left(x + 2\right)^{4}} \left(- x + 4\right) \left(- 3 \sqrt[3]{x} \left(2 x + 4\right) - \left(x + 2\right)^{\left(\frac{2}{x}\right)^{\frac{2}{3}}}\right)$$

Степени

                           /                 2/3                    \
                           |          2/3 /1\                       |
                           |         2   *|-|                       |
  3 ___        2           |              \x/        3 ___          |
  \/ x *(2 + x)    (4 - x)*\- (2 + x)            - 3*\/ x *(4 + 2*x)/
- -------------- + --------------------------------------------------
        3                              2/3        4                  
                                    9*x   *(2 + x)                   

$$- \frac{\sqrt[3]{x}}{3} \left(x + 2\right)^{2} + \frac{1}{9 x^{\frac{2}{3}} \left(x + 2\right)^{4}} \left(- x + 4\right) \left(- 3 \sqrt[3]{x} \left(2 x + 4\right) - \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}}\right)$$

                           /                 2/3                    \
                           |          2/3 /1\                       |
                           |         2   *|-|                       |
  3 ___        2           |              \x/      3 ___            |
  \/ x *(2 + x)    (4 - x)*\- (2 + x)            + \/ x *(-12 - 6*x)/
- -------------- + --------------------------------------------------
        3                              2/3        4                  
                                    9*x   *(2 + x)                   

$$- \frac{\sqrt[3]{x}}{3} \left(x + 2\right)^{2} + \frac{1}{9 x^{\frac{2}{3}} \left(x + 2\right)^{4}} \left(- x + 4\right) \left(\sqrt[3]{x} \left(- 6 x - 12\right) - \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}}\right)$$

Численный ответ

-0.333333333333333*x^0.333333333333333*(2.0 + x)^2 + 0.111111111111111*x^(-0.666666666666667)*(4.0 - x)*(-(2.0 + x)^(1.5874010519682*(1/x)^0.666666666666667) - 3.0*x^0.333333333333333*(4.0 + 2.0*x))/(2.0 + x)^4

Рациональный знаменатель

                                          2/3                                               2/3
                                   2/3 /1\                                           2/3 /1\   
                                  2   *|-|                                          2   *|-|   
      3 ___       4/3                  \x/          7/3              6                   \x/   
- 144*\/ x  - 36*x    - 12*(2 + x)            + 18*x    - 9*x*(2 + x)  + 3*x*(2 + x)           
-----------------------------------------------------------------------------------------------
                                            2/3        4                                       
                                        27*x   *(2 + x)                                        

$$\frac{1}{27 x^{\frac{2}{3}} \left(x + 2\right)^{4}} \left(18 x^{\frac{7}{3}} - 36 x^{\frac{4}{3}} - 144 \sqrt[3]{x} - 9 x \left(x + 2\right)^{6} + 3 x \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}} - 12 \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}}\right)$$

Объединение рациональных выражений

        /                 2/3                  \               
        |          2/3 /1\                     |               
        |         2   *|-|                     |               
        |              \x/        3 ___        |              6
(4 - x)*\- (2 + x)            - 6*\/ x *(2 + x)/ - 3*x*(2 + x) 
---------------------------------------------------------------
                           2/3        4                        
                        9*x   *(2 + x)                         

$$\frac{1}{9 x^{\frac{2}{3}} \left(x + 2\right)^{4}} \left(- 3 x \left(x + 2\right)^{6} + \left(- x + 4\right) \left(- 6 \sqrt[3]{x} \left(x + 2\right) - \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}}\right)\right)$$

Общее упрощение

         /               2/3                  \               
         |        2/3 /1\                     |               
         |       2   *|-|                     |               
         |            \x/        3 ___        |              6
(-4 + x)*\(2 + x)            + 6*\/ x *(2 + x)/ - 3*x*(2 + x) 
--------------------------------------------------------------
                          2/3        4                        
                       9*x   *(2 + x)                         

$$\frac{1}{9 x^{\frac{2}{3}} \left(x + 2\right)^{4}} \left(- 3 x \left(x + 2\right)^{6} + \left(x - 4\right) \left(6 \sqrt[3]{x} \left(x + 2\right) + \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}}\right)\right)$$

Общий знаменатель

 /                                   2/3                                                                                             2/3\ 
 |                            2/3 /1\                                                                                         2/3 /1\   | 
 |                           2   *|-|                                                                                        2   *|-|   | 
 |     7/3      7                 \x/          4/3       6      3 ___        5                4        2        3                 \x/   | 
-\- 6*x    + 3*x  + 4*(2 + x)            + 12*x    + 36*x  + 48*\/ x  + 180*x  + 192*x + 480*x  + 576*x  + 720*x  - x*(2 + x)           / 
------------------------------------------------------------------------------------------------------------------------------------------
                                              14/3       11/3        2/3        8/3        5/3                                            
                                           9*x     + 72*x     + 144*x    + 216*x    + 288*x                                               

$$- \frac{1}{9 x^{\frac{14}{3}} + 72 x^{\frac{11}{3}} + 216 x^{\frac{8}{3}} + 288 x^{\frac{5}{3}} + 144 x^{\frac{2}{3}}} \left(- 6 x^{\frac{7}{3}} + 12 x^{\frac{4}{3}} + 48 \sqrt[3]{x} + 3 x^{7} + 36 x^{6} + 180 x^{5} + 480 x^{4} + 720 x^{3} + 576 x^{2} - x \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}} + 192 x + 4 \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}}\right)$$

Комбинаторика

 /                                   2/3                                                                                             2/3\ 
 |                            2/3 /1\                                                                                         2/3 /1\   | 
 |                           2   *|-|                                                                                        2   *|-|   | 
 |     7/3      7                 \x/          4/3       6      3 ___        5                4        2        3                 \x/   | 
-\- 6*x    + 3*x  + 4*(2 + x)            + 12*x    + 36*x  + 48*\/ x  + 180*x  + 192*x + 480*x  + 576*x  + 720*x  - x*(2 + x)           / 
------------------------------------------------------------------------------------------------------------------------------------------
                                                                2/3        4                                                              
                                                             9*x   *(2 + x)                                                               

$$- \frac{1}{9 x^{\frac{2}{3}} \left(x + 2\right)^{4}} \left(- 6 x^{\frac{7}{3}} + 12 x^{\frac{4}{3}} + 48 \sqrt[3]{x} + 3 x^{7} + 36 x^{6} + 180 x^{5} + 480 x^{4} + 720 x^{3} + 576 x^{2} - x \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}} + 192 x + 4 \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}}\right)$$

Раскрыть выражение

                           /                 2/3                    \
                           |          2/3 /1\                       |
                           |         2   *|-|                       |
 3 ___                     |              \x/        3 ___          |
-\/ x          2   (4 - x)*\- (x + 2)            - 3*\/ x *(4 + 2*x)/
-------*(x + 2)  + --------------------------------------------------
   3                                   2/3        4                  
                                    9*x   *(x + 2)                   

$$- \frac{\sqrt[3]{x}}{3} \left(x + 2\right)^{2} + \frac{1}{9 x^{\frac{2}{3}} \left(x + 2\right)^{4}} \left(- x + 4\right) \left(- 3 \sqrt[3]{x} \left(2 x + 4\right) - \left(x + 2\right)^{2^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}}\right)$$