Общий знаменатель ((36*p^2/10^6+0.0108*p+36 ... +60))+1/25)/(20+10+p/100)

Вы ввели

      2                          
  36*p                           
 ------- + 0.0108*p + 3600       
 1000000                       1 
---------------------------- + --
  /     2                  \   25
  |  3*p                   |     
p*|-------- + 0.0109*p + 60|     
  \10000000                /     
---------------------------------
                   p             
             30 + ---            
                  100            

$$\frac{1}{\frac{p}{100} + 30} \left(\frac{1}{25} + \frac{0.0108 p + \frac{36 p^{2}}{1000000} + 3600}{p \left(0.0109 p + \frac{3 p^{2}}{10000000} + 60\right)}\right)$$

Степени

                  2              
               9*p               
       3600 + ------ + 0.0108*p  
1             250000             
-- + ----------------------------
25     /          2             \
       |       3*p              |
     p*|60 + -------- + 0.0109*p|
       \     10000000           /
---------------------------------
                   p             
             30 + ---            
                  100            

$$\frac{1}{\frac{p}{100} + 30} \left(\frac{1}{25} + \frac{\frac{9 p^{2}}{250000} + 0.0108 p + 3600}{p \left(\frac{3 p^{2}}{10000000} + 0.0109 p + 60\right)}\right)$$

Численный ответ

(0.04 + (3600.0 + 0.0108*p + 3.6e-5*p^2)/(p*(60.0 + 0.0109*p + 3.0e-7*p^2)))/(30.0 + 0.01*p)

Рациональный знаменатель

                                     2                                     /               2             \
90000000000000000000 + 900000000000*p  + 270000000000000.0*p + 100000000*p*\600000000 + 3*p  + 109000.0*p/
----------------------------------------------------------------------------------------------------------
                                                /               2             \                           
                          25000000*p*(3000 + p)*\600000000 + 3*p  + 109000.0*p/                           

$$\frac{900000000000 p^{2} + 100000000 p \left(3 p^{2} + 109000.0 p + 600000000\right) + 270000000000000.0 p + 90000000000000000000}{25000000 p \left(p + 3000\right) \left(3 p^{2} + 109000.0 p + 600000000\right)}$$

Объединение рациональных выражений

4*(900000000000 + p*(600000000 + p*(109000.0 + 3*p)) + 1000*p*(2700.0 + 9*p))
-----------------------------------------------------------------------------
                p*(3000 + p)*(600000000 + p*(109000.0 + 3*p))                

$$\frac{4000 p \left(9 p + 2700.0\right) + 4 p \left(p \left(3 p + 109000.0\right) + 600000000\right) + 3600000000000}{p \left(p + 3000\right) \left(p \left(3 p + 109000.0\right) + 600000000\right)}$$

Общее упрощение

    /                        3             2                 \
1.0*\3600000000000.0 + 12.0*p  + 472000.0*p  + 2410800000.0*p/
--------------------------------------------------------------
    /                       3             2                \  
  p*\1800000000000.0 + 3.0*p  + 118000.0*p  + 927000000.0*p/  

$$\frac{12.0 p^{3} + 472000.0 p^{2} + 2410800000.0 p + 3600000000000.0}{p \left(3.0 p^{3} + 118000.0 p^{2} + 927000000.0 p + 1800000000000.0\right)}$$

Комбинаторика

    /                      3             2                \
4.0*\900000000000.0 + 3.0*p  + 118000.0*p  + 602700000.0*p/
-----------------------------------------------------------
                   /                   2             \     
      p*(3000 + p)*\600000000.0 + 3.0*p  + 109000.0*p/     

$$\frac{12.0 p^{3} + 472000.0 p^{2} + 2410800000.0 p + 3600000000000.0}{p \left(p + 3000\right) \left(3.0 p^{2} + 109000.0 p + 600000000.0\right)}$$

Общий знаменатель

    /                          3               2                  \
1.0*\90000000000000.0 + 300.0*p  + 11800000.0*p  + 60270000000.0*p/
-------------------------------------------------------------------
         4              3                  2                       
   75.0*p  + 2950000.0*p  + 23175000000.0*p  + 45000000000000.0*p  

$$\frac{300.0 p^{3} + 11800000.0 p^{2} + 60270000000.0 p + 90000000000000.0}{75.0 p^{4} + 2950000.0 p^{3} + 23175000000.0 p^{2} + 45000000000000.0 p}$$