(b^(5/4)*c^(1/4)+b^(1/4)*c^(5/4))*1/(b^(5/4))*c^(5/4) если c=-1/2 (упростите выражение)

Выражение, которое надо упростить:

Решение

Вы ввели
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[text]
 5/4 4 ___   4 ___  5/4     
b   *\/ c  + \/ b *c     5/4
-----------------------*c   
           5/4              
          b                 
$$c^{\frac{5}{4}} \frac{1}{b^{\frac{5}{4}}} \left(b^{\frac{5}{4}} \sqrt[4]{c} + \sqrt[4]{b} c^{\frac{5}{4}}\right)$$
Подстановка условия
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((b^(5/4)*c^(1/4) + b^(1/4)*c^(5/4))/b^(5/4))*c^(5/4) при c = -1/2
((b^(5/4)*c^(1/4) + b^(1/4)*c^(5/4))/b^(5/4))*c^(5/4)
$$c^{\frac{5}{4}} \frac{1}{b^{\frac{5}{4}}} \left(b^{\frac{5}{4}} \sqrt[4]{c} + \sqrt[4]{b} c^{\frac{5}{4}}\right)$$
((b^(5/4)*(-1/2)^(1/4) + b^(1/4)*(-1/2)^(5/4))/b^(5/4))*(-1/2)^(5/4)
$$(-1/2)^{\frac{5}{4}} \frac{1}{b^{\frac{5}{4}}} \left((-1/2)^{\frac{5}{4}} \sqrt[4]{b} + \sqrt[4]{(-1/2)} b^{\frac{5}{4}}\right)$$
((b^(5/4)*(-1/2)^(1/4) + b^(1/4)*(-1/2)^(5/4))/b^(5/4))*(-1/2)^(5/4)
$$\left(- \frac{1}{2}\right)^{\frac{5}{4}} \frac{1}{b^{\frac{5}{4}}} \left(\sqrt[4]{- \frac{1}{2}} b^{\frac{5}{4}} + \left(- \frac{1}{2}\right)^{\frac{5}{4}} \sqrt[4]{b}\right)$$
-(-1)^(1/4)*2^(3/4)*((-1)^(1/4)*2^(3/4)*b^(5/4)/2 - (-1)^(1/4)*2^(3/4)*b^(1/4)/4)/(4*b^(5/4))
$$- \frac{\sqrt[4]{-1} \cdot 2^{\frac{3}{4}}}{4 b^{\frac{5}{4}}} \left(\frac{\sqrt[4]{-1} b^{\frac{5}{4}}}{2} 2^{\frac{3}{4}} - \frac{\sqrt[4]{-1} \sqrt[4]{b}}{4} 2^{\frac{3}{4}}\right)$$
Степени
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 5/4 /4 ___  5/4    5/4 4 ___\
c   *\\/ b *c    + b   *\/ c /
------------------------------
              5/4             
             b                
$$\frac{c^{\frac{5}{4}}}{b^{\frac{5}{4}}} \left(b^{\frac{5}{4}} \sqrt[4]{c} + \sqrt[4]{b} c^{\frac{5}{4}}\right)$$
Численный ответ
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b^(-1.25)*c^1.25*(b^0.25*c^1.25 + b^1.25*c^0.25)
Рациональный знаменатель
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 5/4 /4 ___  5/4    5/4 4 ___\
c   *\\/ b *c    + b   *\/ c /
------------------------------
              5/4             
             b                
$$\frac{c^{\frac{5}{4}}}{b^{\frac{5}{4}}} \left(b^{\frac{5}{4}} \sqrt[4]{c} + \sqrt[4]{b} c^{\frac{5}{4}}\right)$$
Объединение рациональных выражений
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 3/2        
c   *(b + c)
------------
     b      
$$\frac{c^{\frac{3}{2}}}{b} \left(b + c\right)$$
Общее упрощение
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 3/2        
c   *(b + c)
------------
     b      
$$\frac{c^{\frac{3}{2}}}{b} \left(b + c\right)$$
Собрать выражение
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[pretty]
[text]
 5/4 /4 ___  5/4    5/4 4 ___\
c   *\\/ b *c    + b   *\/ c /
------------------------------
              5/4             
             b                
$$\frac{c^{\frac{5}{4}}}{b^{\frac{5}{4}}} \left(b^{\frac{5}{4}} \sqrt[4]{c} + \sqrt[4]{b} c^{\frac{5}{4}}\right)$$
Комбинаторика
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[text]
 3/2        
c   *(b + c)
------------
     b      
$$\frac{c^{\frac{3}{2}}}{b} \left(b + c\right)$$
Общий знаменатель
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        5/2
 3/2   c   
c    + ----
        b  
$$c^{\frac{3}{2}} + \frac{c^{\frac{5}{2}}}{b}$$