Общий знаменатель (1/2+(1/2+1/(4*sqrt(x)))/ ... )/sqrt(x+sqrt(x+sqrt(x)))

Вы ввели

        1      1        
        - + -------     
        2       ___     
  1         4*\/ x      
  - + ----------------  
  2        ___________  
          /       ___   
      2*\/  x + \/ x    
------------------------
    ____________________
   /        ___________ 
  /        /       ___  
\/   x + \/  x + \/ x   

$$\frac{\frac{\frac{1}{2} + \frac{1}{4 \sqrt{x}}}{2 \sqrt{\sqrt{x} + x}} + \frac{1}{2}}{\sqrt{x + \sqrt{\sqrt{x} + x}}}$$

Степени

        1      1        
        - + -------     
        4       ___     
   1        8*\/ x      
   - + --------------   
   2      ___________   
         /       ___    
       \/  x + \/ x     
------------------------
    ____________________
   /        ___________ 
  /        /       ___  
\/   x + \/  x + \/ x   

$$\frac{\frac{\frac{1}{4} + \frac{1}{8 \sqrt{x}}}{\sqrt{\sqrt{x} + x}} + \frac{1}{2}}{\sqrt{x + \sqrt{\sqrt{x} + x}}}$$

Численный ответ

(x + (x + x^0.5)^0.5)^(-0.5)*(0.5 + 0.5*(x + x^0.5)^(-0.5)*(0.5 + 0.25*x^(-0.5)))

Рациональный знаменатель

              ____________________             ____________________               ____________________            ____________________              ____________________             ____________________                ____________________               ____________________                            ____________________                              ____________________                              ____________________                           ____________________                           ____________________                             ____________________                            ____________________                            ____________________                              ____________________                              ____________________
             /        ___________             /        ___________               /        ___________            /        ___________              /        ___________             /        ___________                /        ___________               /        ___________                     3/2    /        ___________                       3/2    /        ___________               ___________    /        ___________            ___________    /        ___________            ___________    /        ___________              ___________    /        ___________             ___________    /        ___________                     3/2    /        ___________                       3/2    /        ___________                       3/2    /        ___________ 
      9/2   /        /       ___         3   /        /       ___         5/2   /        /       ___        2   /        /       ___        3/2   /        /       ___         4   /        /       ___         11/2   /        /       ___         7/2   /        /       ___         2 /      ___\      /        /       ___         7/2 /      ___\      /        /       ___         7/2   /       ___    /        /       ___        2   /       ___    /        /       ___        4   /       ___    /        /       ___        9/2   /       ___    /        /       ___         3   /       ___    /        /       ___         3 /      ___\      /        /       ___         3/2 /      ___\      /        /       ___         5/2 /      ___\      /        /       ___  
- 40*x   *\/   x + \/  x + \/ x    - 16*x *\/   x + \/  x + \/ x    - 12*x   *\/   x + \/  x + \/ x    + 4*x *\/   x + \/  x + \/ x    + 4*x   *\/   x + \/  x + \/ x    + 12*x *\/   x + \/  x + \/ x    + 16*x    *\/   x + \/  x + \/ x    + 32*x   *\/   x + \/  x + \/ x    - 32*x *\x + \/ x /   *\/   x + \/  x + \/ x    - 16*x   *\x + \/ x /   *\/   x + \/  x + \/ x    - 12*x   *\/  x + \/ x  *\/   x + \/  x + \/ x    - 4*x *\/  x + \/ x  *\/   x + \/  x + \/ x    - 4*x *\/  x + \/ x  *\/   x + \/  x + \/ x    + 8*x   *\/  x + \/ x  *\/   x + \/  x + \/ x    + 12*x *\/  x + \/ x  *\/   x + \/  x + \/ x    + 16*x *\x + \/ x /   *\/   x + \/  x + \/ x    + 16*x   *\x + \/ x /   *\/   x + \/  x + \/ x    + 16*x   *\x + \/ x /   *\/   x + \/  x + \/ x   
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                                                                                                                                                                                                                                                                                                                                                                              ___ / 2    \ / 2    4          3\                                                                                                                                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                                                                                                                                         32*\/ x *\x  - x/*\x  + x  - x - 2*x /                                                                                                                                                                                                                                                                                                                                                                        

$$\frac{1}{32 \sqrt{x} \left(x^{2} - x\right) \left(x^{4} - 2 x^{3} + x^{2} - x\right)} \left(16 x^{\frac{11}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} + 8 x^{\frac{9}{2}} \sqrt{\sqrt{x} + x} \sqrt{x + \sqrt{\sqrt{x} + x}} - 40 x^{\frac{9}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} - 16 x^{\frac{7}{2}} \left(\sqrt{x} + x\right)^{\frac{3}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} - 12 x^{\frac{7}{2}} \sqrt{\sqrt{x} + x} \sqrt{x + \sqrt{\sqrt{x} + x}} + 32 x^{\frac{7}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} + 16 x^{\frac{5}{2}} \left(\sqrt{x} + x\right)^{\frac{3}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} - 12 x^{\frac{5}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} + 16 x^{\frac{3}{2}} \left(\sqrt{x} + x\right)^{\frac{3}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} + 4 x^{\frac{3}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} - 4 x^{4} \sqrt{\sqrt{x} + x} \sqrt{x + \sqrt{\sqrt{x} + x}} + 12 x^{4} \sqrt{x + \sqrt{\sqrt{x} + x}} + 16 x^{3} \left(\sqrt{x} + x\right)^{\frac{3}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} + 12 x^{3} \sqrt{\sqrt{x} + x} \sqrt{x + \sqrt{\sqrt{x} + x}} - 16 x^{3} \sqrt{x + \sqrt{\sqrt{x} + x}} - 32 x^{2} \left(\sqrt{x} + x\right)^{\frac{3}{2}} \sqrt{x + \sqrt{\sqrt{x} + x}} - 4 x^{2} \sqrt{\sqrt{x} + x} \sqrt{x + \sqrt{\sqrt{x} + x}} + 4 x^{2} \sqrt{x + \sqrt{\sqrt{x} + x}}\right)$$

Объединение рациональных выражений

                               ___________     
              ___       ___   /       ___      
      1 + 2*\/ x  + 4*\/ x *\/  x + \/ x       
-----------------------------------------------
                           ____________________
           ___________    /        ___________ 
    ___   /       ___    /        /       ___  
8*\/ x *\/  x + \/ x  *\/   x + \/  x + \/ x   

$$\frac{4 \sqrt{x} \sqrt{\sqrt{x} + x} + 2 \sqrt{x} + 1}{8 \sqrt{x} \sqrt{\sqrt{x} + x} \sqrt{x + \sqrt{\sqrt{x} + x}}}$$

Общее упрощение

                               ___________     
              ___       ___   /       ___      
      1 + 2*\/ x  + 4*\/ x *\/  x + \/ x       
-----------------------------------------------
                           ____________________
           ___________    /        ___________ 
    ___   /       ___    /        /       ___  
8*\/ x *\/  x + \/ x  *\/   x + \/  x + \/ x   

$$\frac{4 \sqrt{x} \sqrt{\sqrt{x} + x} + 2 \sqrt{x} + 1}{8 \sqrt{x} \sqrt{\sqrt{x} + x} \sqrt{x + \sqrt{\sqrt{x} + x}}}$$

Комбинаторика

                               ___________     
              ___       ___   /       ___      
      1 + 2*\/ x  + 4*\/ x *\/  x + \/ x       
-----------------------------------------------
                           ____________________
           ___________    /        ___________ 
    ___   /       ___    /        /       ___  
8*\/ x *\/  x + \/ x  *\/   x + \/  x + \/ x   

$$\frac{4 \sqrt{x} \sqrt{\sqrt{x} + x} + 2 \sqrt{x} + 1}{8 \sqrt{x} \sqrt{\sqrt{x} + x} \sqrt{x + \sqrt{\sqrt{x} + x}}}$$

Общий знаменатель

                               ___________     
              ___       ___   /       ___      
      1 + 2*\/ x  + 4*\/ x *\/  x + \/ x       
-----------------------------------------------
                           ____________________
           ___________    /        ___________ 
    ___   /       ___    /        /       ___  
8*\/ x *\/  x + \/ x  *\/   x + \/  x + \/ x   

$$\frac{4 \sqrt{x} \sqrt{\sqrt{x} + x} + 2 \sqrt{x} + 1}{8 \sqrt{x} \sqrt{\sqrt{x} + x} \sqrt{x + \sqrt{\sqrt{x} + x}}}$$