Общий знаменатель (-1+1/(3*(x+1)^(2/3)))/(t ... (x)^2-2*x)/(tan(x)+x^2)^2

Вы ввели

          1                                             
-1 + ------------                                       
              2/3   /3 _______    \ /        2         \
     3*(x + 1)      \\/ x + 1  - x/*\-1 - tan (x) - 2*x/
----------------- + ------------------------------------
             2                              2           
   tan(x) + x                  /          2\            
                               \tan(x) + x /            

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

Степени

          1                                             
-1 + ------------                                       
              2/3   /3 _______    \ /        2         \
     3*(1 + x)      \\/ 1 + x  - x/*\-1 - tan (x) - 2*x/
----------------- + ------------------------------------
    2                                       2           
   x  + tan(x)                 / 2         \            
                               \x  + tan(x)/            

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

Численный ответ

(-1.0 + 0.333333333333333*(1.0 + x)^(-0.666666666666667))/(x^2 + tan(x)) + ((1.0 + x)^0.333333333333333 - x)*(-1.0 - tan(x)^2 - 2.0*x)/(x^2 + tan(x))^2

Рациональный знаменатель

             2                                                                                     
/ 2         \  /             2/3\            2/3 / 2         \ /3 _______    \ /        2         \
\x  + tan(x)/ *\1 - 3*(1 + x)   / + 3*(1 + x)   *\x  + tan(x)/*\\/ 1 + x  - x/*\-1 - tan (x) - 2*x/
---------------------------------------------------------------------------------------------------
                                                              3                                    
                                             2/3 / 2         \                                     
                                    3*(1 + x)   *\x  + tan(x)/                                     

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

Объединение рациональных выражений

/             2/3\ / 2         \            2/3 /3 _______    \ /        2         \
\1 - 3*(1 + x)   /*\x  + tan(x)/ + 3*(1 + x)   *\\/ 1 + x  - x/*\-1 - tan (x) - 2*x/
------------------------------------------------------------------------------------
                                                      2                             
                                     2/3 / 2         \                              
                            3*(1 + x)   *\x  + tan(x)/                              

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

Общее упрощение

/             2/3\ / 2         \                                             
\1 - 3*(1 + x)   /*\x  + tan(x)/          2/3 /    3 _______\ /   1         \
-------------------------------- + (1 + x)   *\x - \/ 1 + x /*|------- + 2*x|
               3                                              |   2         |
                                                              \cos (x)      /
-----------------------------------------------------------------------------
                                                  2                          
                                 2/3 / 2         \                           
                          (1 + x)   *\x  + tan(x)/                           

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

Собрать выражение

                                                                                           3 _______                          2                           2                   3 _______    2                     3 _______       
                  1                          1                    x                        \/ 1 + x                        2*x                       x*tan (x)                \/ 1 + x *tan (x)              2*x*\/ 1 + x        
------------------------------------- - ----------- + -------------------------- - -------------------------- + -------------------------- + -------------------------- - -------------------------- - --------------------------
   2        2/3            2/3           2             4      2         2           4      2         2           4      2         2           4      2         2           4      2         2           4      2         2       
3*x *(1 + x)    + 3*(1 + x)   *tan(x)   x  + tan(x)   x  + tan (x) + 2*x *tan(x)   x  + tan (x) + 2*x *tan(x)   x  + tan (x) + 2*x *tan(x)   x  + tan (x) + 2*x *tan(x)   x  + tan (x) + 2*x *tan(x)   x  + tan (x) + 2*x *tan(x)

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

Комбинаторика

              2        2             2               2/3                     2/3      2        2/3              2/3    2            
-3 - 9*x - 5*x  - 3*tan (x) - 3*x*tan (x) - 3*(1 + x)   *tan(x) + 3*x*(1 + x)    + 3*x *(1 + x)    + 3*x*(1 + x)   *tan (x) + tan(x)
------------------------------------------------------------------------------------------------------------------------------------
                                                                              2                                                     
                                                             2/3 / 2         \                                                      
                                                    3*(1 + x)   *\x  + tan(x)/                                                      

$$\frac{1}{3 \left(x + 1\right)^{\frac{2}{3}} \left(x^{2} + \tan{\left (x \right )}\right)^{2}} \left(3 x^{2} \left(x + 1\right)^{\frac{2}{3}} - 5 x^{2} + 3 x \left(x + 1\right)^{\frac{2}{3}} \tan^{2}{\left (x \right )} + 3 x \left(x + 1\right)^{\frac{2}{3}} - 3 x \tan^{2}{\left (x \right )} - 9 x - 3 \left(x + 1\right)^{\frac{2}{3}} \tan{\left (x \right )} - 3 \tan^{2}{\left (x \right )} + \tan{\left (x \right )} - 3\right)$$

Общий знаменатель

              2        2             2               2/3                     2/3      2        2/3              2/3    2            
-3 - 9*x - 5*x  - 3*tan (x) - 3*x*tan (x) - 3*(1 + x)   *tan(x) + 3*x*(1 + x)    + 3*x *(1 + x)    + 3*x*(1 + x)   *tan (x) + tan(x)
------------------------------------------------------------------------------------------------------------------------------------
                                     4        2/3            2/3    2         2        2/3                                          
                                  3*x *(1 + x)    + 3*(1 + x)   *tan (x) + 6*x *(1 + x)   *tan(x)                                   

$$\frac{1}{3 x^{4} \left(x + 1\right)^{\frac{2}{3}} + 6 x^{2} \left(x + 1\right)^{\frac{2}{3}} \tan{\left (x \right )} + 3 \left(x + 1\right)^{\frac{2}{3}} \tan^{2}{\left (x \right )}} \left(3 x^{2} \left(x + 1\right)^{\frac{2}{3}} - 5 x^{2} + 3 x \left(x + 1\right)^{\frac{2}{3}} \tan^{2}{\left (x \right )} + 3 x \left(x + 1\right)^{\frac{2}{3}} - 3 x \tan^{2}{\left (x \right )} - 9 x - 3 \left(x + 1\right)^{\frac{2}{3}} \tan{\left (x \right )} - 3 \tan^{2}{\left (x \right )} + \tan{\left (x \right )} - 3\right)$$

Тригонометрическая часть

          1         /    3 _______\ /   1         \
-1 + ------------   \x - \/ x + 1 /*|------- + 2*x|
              2/3                   |   2         |
     3*(x + 1)                      \cos (x)      /
----------------- + -------------------------------
             2                            2        
   tan(x) + x                / 2         \         
                             \x  + tan(x)/         

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

Раскрыть выражение

          1                                             
-1 + ------------                                       
              2/3   /3 _______    \ /        2         \
     3*(1 + x)      \\/ 1 + x  - x/*\-1 - tan (x) - 2*x/
----------------- + ------------------------------------
    2                                       2           
   x  + tan(x)                 / 2         \            
                               \x  + tan(x)/            

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