Общий знаменатель -21/(x-4)^8-(-2+5*x)/sqrt(5*x^2-4*x+3)

Вы ввели

     21            -2 + 5*x     
- -------- - -------------------
         8      ________________
  (x - 4)      /    2           
             \/  5*x  - 4*x + 3 

$$- \frac{5 x - 2}{\sqrt{5 x^{2} - 4 x + 3}} - \frac{21}{\left(x - 4\right)^{8}}$$

Степени

      21            2 - 5*x      
- --------- + -------------------
          8      ________________
  (-4 + x)      /              2 
              \/  3 - 4*x + 5*x  

$$\frac{- 5 x + 2}{\sqrt{5 x^{2} - 4 x + 3}} - \frac{21}{\left(x - 4\right)^{8}}$$

Численный ответ

-21.0/(-4.0 + x)^8 - (3.0 + 5.0*x^2 - 4.0*x)^(-0.5)*(-2.0 + 5.0*x)

Рациональный знаменатель

        ________________                              
       /              2              8               8
- 21*\/  3 - 4*x + 5*x   + 2*(-4 + x)  - 5*x*(-4 + x) 
------------------------------------------------------
                         ________________             
                    8   /              2              
            (-4 + x) *\/  3 - 4*x + 5*x               

$$\frac{- 5 x \left(x - 4\right)^{8} + 2 \left(x - 4\right)^{8} - 21 \sqrt{5 x^{2} - 4 x + 3}}{\left(x - 4\right)^{8} \sqrt{5 x^{2} - 4 x + 3}}$$

Объединение рациональных выражений

       __________________           8           
- 21*\/ 3 + x*(-4 + 5*x)  - (-4 + x) *(-2 + 5*x)
------------------------------------------------
                 8   __________________         
         (-4 + x) *\/ 3 + x*(-4 + 5*x)          

$$\frac{- \left(x - 4\right)^{8} \left(5 x - 2\right) - 21 \sqrt{x \left(5 x - 4\right) + 3}}{\left(x - 4\right)^{8} \sqrt{x \left(5 x - 4\right) + 3}}$$

Общее упрощение

      21               2                    5*x        
- --------- + ------------------- - -------------------
          8      ________________      ________________
  (-4 + x)      /              2      /              2 
              \/  3 - 4*x + 5*x     \/  3 - 4*x + 5*x  

$$- \frac{5 x}{\sqrt{5 x^{2} - 4 x + 3}} + \frac{2}{\sqrt{5 x^{2} - 4 x + 3}} - \frac{21}{\left(x - 4\right)^{8}}$$

Комбинаторика

 /                                                                   ________________                                            \ 
 |                  2           4          6        8      9        /              2          7          5                      3| 
-\-131072 - 884736*x  - 322560*x  - 18816*x  - 162*x  + 5*x  + 21*\/  3 - 4*x + 5*x   + 2304*x  + 96768*x  + 589824*x + 688128*x / 
-----------------------------------------------------------------------------------------------------------------------------------
                                                                ________________                                                   
                                                           8   /              2                                                    
                                                   (-4 + x) *\/  3 - 4*x + 5*x                                                     

$$- \frac{1}{\left(x - 4\right)^{8} \sqrt{5 x^{2} - 4 x + 3}} \left(5 x^{9} - 162 x^{8} + 2304 x^{7} - 18816 x^{6} + 96768 x^{5} - 322560 x^{4} + 688128 x^{3} - 884736 x^{2} + 589824 x + 21 \sqrt{5 x^{2} - 4 x + 3} - 131072\right)$$

Общий знаменатель

                                                                  /                                                                   ________________                                            \                                                                   
                                                                  |                  2           4          6        8      9        /              2          7          5                      3|                                                                   
                                                                 -\-131072 - 884736*x  - 322560*x  - 18816*x  - 162*x  + 5*x  + 21*\/  3 - 4*x + 5*x   + 2304*x  + 96768*x  + 589824*x + 688128*x /                                                                   
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         ________________         ________________               ________________               ________________              ________________            ________________             ________________               ________________                ________________
        /              2     8   /              2               /              2           3   /              2          5   /              2        7   /              2         6   /              2           4   /              2            2   /              2 
65536*\/  3 - 4*x + 5*x   + x *\/  3 - 4*x + 5*x   - 131072*x*\/  3 - 4*x + 5*x   - 57344*x *\/  3 - 4*x + 5*x   - 3584*x *\/  3 - 4*x + 5*x   - 32*x *\/  3 - 4*x + 5*x   + 448*x *\/  3 - 4*x + 5*x   + 17920*x *\/  3 - 4*x + 5*x   + 114688*x *\/  3 - 4*x + 5*x  

$$- \frac{5 x^{9} - 162 x^{8} + 2304 x^{7} - 18816 x^{6} + 96768 x^{5} - 322560 x^{4} + 688128 x^{3} - 884736 x^{2} + 589824 x + 21 \sqrt{5 x^{2} - 4 x + 3} - 131072}{x^{8} \sqrt{5 x^{2} - 4 x + 3} - 32 x^{7} \sqrt{5 x^{2} - 4 x + 3} + 448 x^{6} \sqrt{5 x^{2} - 4 x + 3} - 3584 x^{5} \sqrt{5 x^{2} - 4 x + 3} + 17920 x^{4} \sqrt{5 x^{2} - 4 x + 3} - 57344 x^{3} \sqrt{5 x^{2} - 4 x + 3} + 114688 x^{2} \sqrt{5 x^{2} - 4 x + 3} - 131072 x \sqrt{5 x^{2} - 4 x + 3} + 65536 \sqrt{5 x^{2} - 4 x + 3}}$$