Калькуляторы онлайн/ Решение уравнений/ Упрощение выражений/ Общий знаменатель/ -21/(sqrt(1-441*x^2)*sqrt(1-4*x+2*x^2))-(-2+2*x)*(acos(21*x)+2)/(1-4*x+2*x^2)^(3/2)

Общий знаменатель -21/(sqrt(1-441*x^2)*sqrt ... x)+2)/(1-4*x+2*x^2)^(3/2)

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Примеры

Решение

Вы ввели [src]
                   21                   (-2 + 2*x)*(acos(21*x) + 2)
- ----------------------------------- - ---------------------------
     ____________    ________________                       3/2    
    /          2    /              2        /             2\       
  \/  1 - 441*x  *\/  1 - 4*x + 2*x         \1 - 4*x + 2*x /
−(2x−2)(acos⁡(21x)+2)(2x2+−4x+1)32−2112x2+−4x+1−441x2+1- \frac{\left(2 x - 2\right) \left(\operatorname{acos}{\left (21 x \right )} + 2\right)}{\left(2 x^{2} + - 4 x + 1\right)^{\frac{3}{2}}} - 21 \frac{1}{\sqrt{2 x^{2} + - 4 x + 1} \sqrt{- 441 x^{2} + 1}}
Степени [src]
                   21                   (-2 + 2*x)*(2 + acos(21*x))
- ----------------------------------- - ---------------------------
     ____________    ________________                       3/2    
    /          2    /              2        /             2\       
  \/  1 - 441*x  *\/  1 - 4*x + 2*x         \1 - 4*x + 2*x /
−(2x−2)(acos⁡(21x)+2)(2x2−4x+1)32−21−441x2+12x2−4x+1- \frac{\left(2 x - 2\right) \left(\operatorname{acos}{\left (21 x \right )} + 2\right)}{\left(2 x^{2} - 4 x + 1\right)^{\frac{3}{2}}} - \frac{21}{\sqrt{- 441 x^{2} + 1} \sqrt{2 x^{2} - 4 x + 1}}
                  21                   (-2 + 2*x)*(2 + acos(21*x))
- ---------------------------------- - ---------------------------
     _______________________________                       3/2    
    / /         2\ /             2\        /             2\       
  \/  \1 - 441*x /*\1 - 4*x + 2*x /        \1 - 4*x + 2*x /
−(2x−2)(acos⁡(21x)+2)(2x2−4x+1)32−21(−441x2+1)(2x2−4x+1)- \frac{\left(2 x - 2\right) \left(\operatorname{acos}{\left (21 x \right )} + 2\right)}{\left(2 x^{2} - 4 x + 1\right)^{\frac{3}{2}}} - \frac{21}{\sqrt{\left(- 441 x^{2} + 1\right) \left(2 x^{2} - 4 x + 1\right)}}
Численный ответ [src]
-21.0*(1.0 - 441.0*x^2)^(-0.5)*(1.0 + 2.0*x^2 - 4.0*x)^(-0.5) - (1.0 + 2.0*x^2 - 4.0*x)^(-1.5)*(2.0 + acos(21*x))*(-2.0 + 2.0*x)
Рациональный знаменатель [src]
       ________________              ________________        ________________                     ________________         ____________                 3/2              ________________             ________________                     ________________                        ________________           
      /              2          3   /              2        /              2                     /              2         /          2  /             2\            2   /              2         3   /              2                     /              2                    2   /              2            
- 4*\/  1 - 4*x + 2*x   - 1764*x *\/  1 - 4*x + 2*x   - 2*\/  1 - 4*x + 2*x  *acos(21*x) + 4*x*\/  1 - 4*x + 2*x   + 21*\/  1 - 441*x  *\1 - 4*x + 2*x /    + 1764*x *\/  1 - 4*x + 2*x   - 882*x *\/  1 - 4*x + 2*x  *acos(21*x) + 2*x*\/  1 - 4*x + 2*x  *acos(21*x) + 882*x *\/  1 - 4*x + 2*x  *acos(21*x)
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                                                                                                                                                                     2                                                                                                                                        
                                                                                                                                       /          2\ /             2\                                                                                                                                         
                                                                                                                                       \-1 + 441*x /*\1 - 4*x + 2*x /
1(441x2−1)(2x2−4x+1)2(−882x32x2−4x+1acos⁡(21x)−1764x32x2−4x+1+882x22x2−4x+1acos⁡(21x)+1764x22x2−4x+1+2x2x2−4x+1acos⁡(21x)+4x2x2−4x+1+21−441x2+1(2x2−4x+1)32−22x2−4x+1acos⁡(21x)−42x2−4x+1)\frac{1}{\left(441 x^{2} - 1\right) \left(2 x^{2} - 4 x + 1\right)^{2}} \left(- 882 x^{3} \sqrt{2 x^{2} - 4 x + 1} \operatorname{acos}{\left (21 x \right )} - 1764 x^{3} \sqrt{2 x^{2} - 4 x + 1} + 882 x^{2} \sqrt{2 x^{2} - 4 x + 1} \operatorname{acos}{\left (21 x \right )} + 1764 x^{2} \sqrt{2 x^{2} - 4 x + 1} + 2 x \sqrt{2 x^{2} - 4 x + 1} \operatorname{acos}{\left (21 x \right )} + 4 x \sqrt{2 x^{2} - 4 x + 1} + 21 \sqrt{- 441 x^{2} + 1} \left(2 x^{2} - 4 x + 1\right)^{\frac{3}{2}} - 2 \sqrt{2 x^{2} - 4 x + 1} \operatorname{acos}{\left (21 x \right )} - 4 \sqrt{2 x^{2} - 4 x + 1}\right)
Объединение рациональных выражений [src]
                          ____________                          
          2              /          2                           
-21 - 42*x  + 84*x - 2*\/  1 - 441*x  *(-1 + x)*(2 + acos(21*x))
----------------------------------------------------------------
                 ____________                 3/2               
                /          2  /             2\                  
              \/  1 - 441*x  *\1 - 4*x + 2*x /
1−441x2+1(2x2−4x+1)32(−42x2+84x−2(x−1)−441x2+1(acos⁡(21x)+2)−21)\frac{1}{\sqrt{- 441 x^{2} + 1} \left(2 x^{2} - 4 x + 1\right)^{\frac{3}{2}}} \left(- 42 x^{2} + 84 x - 2 \left(x - 1\right) \sqrt{- 441 x^{2} + 1} \left(\operatorname{acos}{\left (21 x \right )} + 2\right) - 21\right)
Общее упрощение [src]
                          ____________                          
          2              /          2                           
-21 - 42*x  + 84*x - 2*\/  1 - 441*x  *(-1 + x)*(2 + acos(21*x))
----------------------------------------------------------------
                 ____________                 3/2               
                /          2  /             2\                  
              \/  1 - 441*x  *\1 - 4*x + 2*x /
1−441x2+1(2x2−4x+1)32(−42x2+84x−2(x−1)−441x2+1(acos⁡(21x)+2)−21)\frac{1}{\sqrt{- 441 x^{2} + 1} \left(2 x^{2} - 4 x + 1\right)^{\frac{3}{2}}} \left(- 42 x^{2} + 84 x - 2 \left(x - 1\right) \sqrt{- 441 x^{2} + 1} \left(\operatorname{acos}{\left (21 x \right )} + 2\right) - 21\right)
Собрать выражение [src]
                      1                    (-2 + 2*x)*(acos(21*x) + 2)
- 21*----------------------------------- - ---------------------------
        ____________    ________________                       3/2    
       /          2    /              2        /             2\       
     \/  1 - 441*x  *\/  1 - 4*x + 2*x         \1 - 4*x + 2*x /
−(2x−2)(acos⁡(21x)+2)(2x2+−4x+1)32−212x2+−4x+1−441x2+1- \frac{\left(2 x - 2\right) \left(\operatorname{acos}{\left (21 x \right )} + 2\right)}{\left(2 x^{2} + - 4 x + 1\right)^{\frac{3}{2}}} - \frac{21}{\sqrt{2 x^{2} + - 4 x + 1} \sqrt{- 441 x^{2} + 1}}
Комбинаторика [src]
 /                 ____________                ____________                     ____________          ____________           \ 
 |                /          2        2       /          2                     /          2          /          2            | 
-\21 - 84*x - 4*\/  1 - 441*x   + 42*x  - 2*\/  1 - 441*x  *acos(21*x) + 4*x*\/  1 - 441*x   + 2*x*\/  1 - 441*x  *acos(21*x)/ 
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                                                                                    3/2                                        
                                          _________________________ /             2\                                           
                                        \/ -(1 + 21*x)*(-1 + 21*x) *\1 - 4*x + 2*x /
−1−(21x−1)(21x+1)(2x2−4x+1)32(42x2+2x−441x2+1acos⁡(21x)+4x−441x2+1−84x−2−441x2+1acos⁡(21x)−4−441x2+1+21)- \frac{1}{\sqrt{- \left(21 x - 1\right) \left(21 x + 1\right)} \left(2 x^{2} - 4 x + 1\right)^{\frac{3}{2}}} \left(42 x^{2} + 2 x \sqrt{- 441 x^{2} + 1} \operatorname{acos}{\left (21 x \right )} + 4 x \sqrt{- 441 x^{2} + 1} - 84 x - 2 \sqrt{- 441 x^{2} + 1} \operatorname{acos}{\left (21 x \right )} - 4 \sqrt{- 441 x^{2} + 1} + 21\right)
Общий знаменатель [src]
 /                 ____________                ____________                     ____________          ____________           \ 
 |                /          2        2       /          2                     /          2          /          2            | 
-\21 - 84*x - 4*\/  1 - 441*x   + 42*x  - 2*\/  1 - 441*x  *acos(21*x) + 4*x*\/  1 - 441*x   + 2*x*\/  1 - 441*x  *acos(21*x)/ 
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       ____________    ________________          ____________    ________________           ____________    ________________   
      /          2    /              2          /          2    /              2       2   /          2    /              2    
    \/  1 - 441*x  *\/  1 - 4*x + 2*x   - 4*x*\/  1 - 441*x  *\/  1 - 4*x + 2*x   + 2*x *\/  1 - 441*x  *\/  1 - 4*x + 2*x
−42x2+2x−441x2+1acos⁡(21x)+4x−441x2+1−84x−2−441x2+1acos⁡(21x)−4−441x2+1+212x2−441x2+12x2−4x+1−4x−441x2+12x2−4x+1+−441x2+12x2−4x+1- \frac{42 x^{2} + 2 x \sqrt{- 441 x^{2} + 1} \operatorname{acos}{\left (21 x \right )} + 4 x \sqrt{- 441 x^{2} + 1} - 84 x - 2 \sqrt{- 441 x^{2} + 1} \operatorname{acos}{\left (21 x \right )} - 4 \sqrt{- 441 x^{2} + 1} + 21}{2 x^{2} \sqrt{- 441 x^{2} + 1} \sqrt{2 x^{2} - 4 x + 1} - 4 x \sqrt{- 441 x^{2} + 1} \sqrt{2 x^{2} - 4 x + 1} + \sqrt{- 441 x^{2} + 1} \sqrt{2 x^{2} - 4 x + 1}}
Раскрыть выражение [src]
  (-2 + 2*x)*(acos(21*x) + 2)                    21                
- --------------------------- - -----------------------------------
                      3/2          ____________    ________________
      /             2\            /          2    /              2 
      \1 - 4*x + 2*x /          \/  1 - 441*x  *\/  1 - 4*x + 2*x
−(2x−2)(acos⁡(21x)+2)(2x2+−4x+1)32−212x2+−4x+1−441x2+1- \frac{\left(2 x - 2\right) \left(\operatorname{acos}{\left (21 x \right )} + 2\right)}{\left(2 x^{2} + - 4 x + 1\right)^{\frac{3}{2}}} - \frac{21}{\sqrt{2 x^{2} + - 4 x + 1} \sqrt{- 441 x^{2} + 1}}