Общий знаменатель (((2^tan(x+z)-2^sin(x+z)) ... an(x)-2^sin(x))/(x^2)))/z

Вы ввели

 tan(x + z)    sin(x + z)    tan(x)    sin(x)
2           - 2             2       - 2      
------------------------- - -----------------
                2                    2       
         (x + z)                    x        
---------------------------------------------
                      z                      

$$\frac{1}{z} \left(\frac{1}{\left(x + z\right)^{2}} \left(- 2^{\sin{\left (x + z \right )}} + 2^{\tan{\left (x + z \right )}}\right) - \frac{1}{x^{2}} \left(- 2^{\sin{\left (x \right )}} + 2^{\tan{\left (x \right )}}\right)\right)$$

Численный ответ

((2.0^tan(x + z) - 2.0^sin(x + z))/(x + z)^2 - (2.0^tan(x) - 2.0^sin(x))/x^2)/z

Рациональный знаменатель

 2 / tan(x + z)    sin(x + z)\          2 / sin(x)    tan(x)\
x *\2           - 2          / + (x + z) *\2       - 2      /
-------------------------------------------------------------
                         2          2                        
                        x *z*(x + z)                         

$$\frac{1}{x^{2} z \left(x + z\right)^{2}} \left(x^{2} \left(- 2^{\sin{\left (x + z \right )}} + 2^{\tan{\left (x + z \right )}}\right) + \left(2^{\sin{\left (x \right )}} - 2^{\tan{\left (x \right )}}\right) \left(x + z\right)^{2}\right)$$

Объединение рациональных выражений

 2 / tan(x + z)    sin(x + z)\          2 / tan(x)    sin(x)\
x *\2           - 2          / - (x + z) *\2       - 2      /
-------------------------------------------------------------
                         2          2                        
                        x *z*(x + z)                         

$$\frac{1}{x^{2} z \left(x + z\right)^{2}} \left(x^{2} \left(- 2^{\sin{\left (x + z \right )}} + 2^{\tan{\left (x + z \right )}}\right) - \left(- 2^{\sin{\left (x \right )}} + 2^{\tan{\left (x \right )}}\right) \left(x + z\right)^{2}\right)$$

Общее упрощение

 2 / tan(x + z)    sin(x + z)\          2 / sin(x)    tan(x)\
x *\2           - 2          / + (x + z) *\2       - 2      /
-------------------------------------------------------------
                         2          2                        
                        x *z*(x + z)                         

$$\frac{1}{x^{2} z \left(x + z\right)^{2}} \left(x^{2} \left(- 2^{\sin{\left (x + z \right )}} + 2^{\tan{\left (x + z \right )}}\right) + \left(2^{\sin{\left (x \right )}} - 2^{\tan{\left (x \right )}}\right) \left(x + z\right)^{2}\right)$$

Собрать выражение

    1 + sin(x)             sin(x)             tan(x + z)           1 + tan(x)           sin(x + z)             tan(x)                 sin(x)                tan(x)     
   2                      2                  2                    2                    2                      2                    z*2                   z*2           
------------------ + ------------------ + ------------------ - ------------------ - ------------------ - ------------------ + ------------------- - -------------------
 3      2        2    3      2        2    3      2        2    3      2        2    3      2        2    3      2        2    4    2  2        3    4    2  2        3
x  + x*z  + 2*z*x    z  + z*x  + 2*x*z    z  + z*x  + 2*x*z    x  + x*z  + 2*z*x    z  + z*x  + 2*x*z    z  + z*x  + 2*x*z    x  + x *z  + 2*z*x    x  + x *z  + 2*z*x 

$$\frac{2^{\sin{\left (x \right )} + 1}}{x^{3} + 2 x^{2} z + x z^{2}} - \frac{2^{\tan{\left (x \right )} + 1}}{x^{3} + 2 x^{2} z + x z^{2}} + \frac{2^{\sin{\left (x \right )}} z}{x^{4} + 2 x^{3} z + x^{2} z^{2}} + \frac{2^{\sin{\left (x \right )}}}{x^{2} z + 2 x z^{2} + z^{3}} - \frac{2^{\sin{\left (x + z \right )}}}{x^{2} z + 2 x z^{2} + z^{3}} - \frac{2^{\tan{\left (x \right )}} z}{x^{4} + 2 x^{3} z + x^{2} z^{2}} - \frac{2^{\tan{\left (x \right )}}}{x^{2} z + 2 x z^{2} + z^{3}} + \frac{2^{\tan{\left (x + z \right )}}}{x^{2} z + 2 x z^{2} + z^{3}}$$

Общий знаменатель

 / sin(x + z)  2    tan(x)  2    tan(x)  2    sin(x)  2    sin(x)  2    tan(x + z)  2          sin(x)          tan(x)\ 
-\2          *x  + 2      *x  + 2      *z  - 2      *x  - 2      *z  - 2          *x  - 2*x*z*2       + 2*x*z*2      / 
-----------------------------------------------------------------------------------------------------------------------
                                                    4    2  3      3  2                                                
                                                 z*x  + x *z  + 2*x *z                                                 

$$- \frac{1}{x^{4} z + 2 x^{3} z^{2} + x^{2} z^{3}} \left(- 2^{\sin{\left (x \right )}} x^{2} - 2 \cdot 2^{\sin{\left (x \right )}} x z - 2^{\sin{\left (x \right )}} z^{2} + 2^{\sin{\left (x + z \right )}} x^{2} + 2^{\tan{\left (x \right )}} x^{2} + 2 \cdot 2^{\tan{\left (x \right )}} x z + 2^{\tan{\left (x \right )}} z^{2} - 2^{\tan{\left (x + z \right )}} x^{2}\right)$$

Комбинаторика

 / sin(x + z)  2    tan(x)  2    tan(x)  2    sin(x)  2    sin(x)  2    tan(x + z)  2          sin(x)          tan(x)\ 
-\2          *x  + 2      *x  + 2      *z  - 2      *x  - 2      *z  - 2          *x  - 2*x*z*2       + 2*x*z*2      / 
-----------------------------------------------------------------------------------------------------------------------
                                                      2          2                                                     
                                                     x *z*(x + z)                                                      

$$- \frac{1}{x^{2} z \left(x + z\right)^{2}} \left(- 2^{\sin{\left (x \right )}} x^{2} - 2 \cdot 2^{\sin{\left (x \right )}} x z - 2^{\sin{\left (x \right )}} z^{2} + 2^{\sin{\left (x + z \right )}} x^{2} + 2^{\tan{\left (x \right )}} x^{2} + 2 \cdot 2^{\tan{\left (x \right )}} x z + 2^{\tan{\left (x \right )}} z^{2} - 2^{\tan{\left (x + z \right )}} x^{2}\right)$$

Раскрыть выражение

  tan(x) + tan(z)                                                      
 -----------------                                                     
 1 - tan(x)*tan(z)    cos(x)*sin(z) + cos(z)*sin(x)    tan(x)    sin(x)
2                  - 2                                2       - 2      
--------------------------------------------------- - -----------------
                             2                                 2       
                      (x + z)                                 x        
-----------------------------------------------------------------------
                                   z                                   

$$\frac{1}{z} \left(\frac{1}{\left(x + z\right)^{2}} \left(2^{\frac{\tan{\left (x \right )} + \tan{\left (z \right )}}{- \tan{\left (x \right )} \tan{\left (z \right )} + 1}} - 2^{\sin{\left (x \right )} \cos{\left (z \right )} + \sin{\left (z \right )} \cos{\left (x \right )}}\right) - \frac{1}{x^{2}} \left(- 2^{\sin{\left (x \right )}} + 2^{\tan{\left (x \right )}}\right)\right)$$