Общий знаменатель (-6*cos(6/x)+2*x*sin(6/x))/sqrt(1-x^4*sin(6/x)^2)

Вы ввели

       /6\          /6\
- 6*cos|-| + 2*x*sin|-|
       \x/          \x/
-----------------------
      ________________ 
     /      4    2/6\  
    /  1 - x *sin |-|  
  \/              \x/  

$$\frac{2 x \sin{\left (\frac{6}{x} \right )} - 6 \cos{\left (\frac{6}{x} \right )}}{\sqrt{- x^{4} \sin^{2}{\left (\frac{6}{x} \right )} + 1}}$$

Численный ответ

(1.0 - x^4*sin(6/x)^2)^(-0.5)*(-6.0*cos(6/x) + 2.0*x*sin(6/x))

Рациональный знаменатель

       ________________                        
      /      4    2/6\  /       /6\        /6\\
-2*  /  1 - x *sin |-| *|- 3*cos|-| + x*sin|-||
   \/              \x/  \       \x/        \x//
-----------------------------------------------
                      4    2/6\                
                -1 + x *sin |-|                
                            \x/                

$$- \frac{2 \sqrt{- x^{4} \sin^{2}{\left (\frac{6}{x} \right )} + 1}}{x^{4} \sin^{2}{\left (\frac{6}{x} \right )} - 1} \left(x \sin{\left (\frac{6}{x} \right )} - 3 \cos{\left (\frac{6}{x} \right )}\right)$$

Собрать выражение

            ___    /6\                   ___    /6\    
        6*\/ 2 *cos|-|             2*x*\/ 2 *sin|-|    
                   \x/                          \x/    
- ------------------------- + -------------------------
      _____________________       _____________________
     /      4    4    /12\       /      4    4    /12\ 
    /  2 - x  + x *cos|--|      /  2 - x  + x *cos|--| 
  \/                  \x /    \/                  \x / 

$$\frac{2 \sqrt{2} x \sin{\left (\frac{6}{x} \right )}}{\sqrt{x^{4} \cos{\left (\frac{12}{x} \right )} - x^{4} + 2}} - \frac{6 \sqrt{2} \cos{\left (\frac{6}{x} \right )}}{\sqrt{x^{4} \cos{\left (\frac{12}{x} \right )} - x^{4} + 2}}$$

Комбинаторика

         /       /6\        /6\\       
       2*|- 3*cos|-| + x*sin|-||       
         \       \x/        \x//       
---------------------------------------
    ___________________________________
   /  /     2    /6\\ /      2    /6\\ 
  /  -|1 + x *sin|-||*|-1 + x *sin|-|| 
\/    \          \x// \           \x// 

$$\frac{2 x \sin{\left (\frac{6}{x} \right )} - 6 \cos{\left (\frac{6}{x} \right )}}{\sqrt{- \left(x^{2} \sin{\left (\frac{6}{x} \right )} - 1\right) \left(x^{2} \sin{\left (\frac{6}{x} \right )} + 1\right)}}$$

Раскрыть выражение

       6/1\        6/1\     /        3/1\    3/1\         5/1\    /1\         5/1\    /1\\         2/1\    4/1\         4/1\    2/1\
- 6*cos |-| + 6*sin |-| + x*|- 40*cos |-|*sin |-| + 12*cos |-|*sin|-| + 12*sin |-|*cos|-|| - 90*cos |-|*sin |-| + 90*cos |-|*sin |-|
        \x/         \x/     \         \x/     \x/          \x/    \x/          \x/    \x//          \x/     \x/          \x/     \x/
------------------------------------------------------------------------------------------------------------------------------------
                                 ______________________________________________________________________                             
                                /                                                                    2                              
                               /       4 /        3/1\    3/1\        5/1\    /1\        5/1\    /1\\                               
                              /   1 - x *|- 20*cos |-|*sin |-| + 6*cos |-|*sin|-| + 6*sin |-|*cos|-||                               
                            \/           \         \x/     \x/         \x/    \x/         \x/    \x//                               

$$\frac{x \left(12 \sin^{5}{\left (\frac{1}{x} \right )} \cos{\left (\frac{1}{x} \right )} - 40 \sin^{3}{\left (\frac{1}{x} \right )} \cos^{3}{\left (\frac{1}{x} \right )} + 12 \sin{\left (\frac{1}{x} \right )} \cos^{5}{\left (\frac{1}{x} \right )}\right) + 6 \sin^{6}{\left (\frac{1}{x} \right )} - 90 \sin^{4}{\left (\frac{1}{x} \right )} \cos^{2}{\left (\frac{1}{x} \right )} + 90 \sin^{2}{\left (\frac{1}{x} \right )} \cos^{4}{\left (\frac{1}{x} \right )} - 6 \cos^{6}{\left (\frac{1}{x} \right )}}{\sqrt{- x^{4} \left(6 \sin^{5}{\left (\frac{1}{x} \right )} \cos{\left (\frac{1}{x} \right )} - 20 \sin^{3}{\left (\frac{1}{x} \right )} \cos^{3}{\left (\frac{1}{x} \right )} + 6 \sin{\left (\frac{1}{x} \right )} \cos^{5}{\left (\frac{1}{x} \right )}\right)^{2} + 1}}$$