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Simplificación de expresiones/ Descomposición en fracciones simples/ (sqrt((a*b*c+4)/a+4*(sqrt(b*c)/a)))/(sqrt(a*b*c)+2)

¿Cómo vas a descomponer esta (sqrt((a*b*c+4)/a+4*(sqrt(b*c)/a)))/(sqrt(a*b*c)+2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     _______________________
    /                 _____ 
   /  a*b*c + 4     \/ b*c  
  /   --------- + 4*------- 
\/        a            a    
----------------------------
         _______            
       \/ a*b*c  + 2
4bca+cab+4acab+2\frac{\sqrt{4 \frac{\sqrt{b c}}{a} + \frac{c a b + 4}{a}}}{\sqrt{c a b} + 2} 
sqrt(((a*b)*c + 4)/a + 4*(sqrt(b*c)/a))/(sqrt((a*b)*c) + 2)
Simplificación general [src] 
     _______________________
    /         _____         
   /  4 + 4*\/ b*c  + a*b*c 
  /   --------------------- 
\/              a           
----------------------------
             _______        
       2 + \/ a*b*c
abc+4bc+4aabc+2\frac{\sqrt{\frac{a b c + 4 \sqrt{b c} + 4}{a}}}{\sqrt{a b c} + 2} 
sqrt((4 + 4*sqrt(b*c) + a*b*c)/a)/(2 + sqrt(a*b*c))
Respuesta numérica [src] 
2.0*((b*c)^0.5/a + 0.25*(4.0 + a*b*c)/a)^0.5/(2.0 + (a*b*c)^0.5)
2.0*((b*c)^0.5/a + 0.25*(4.0 + a*b*c)/a)^0.5/(2.0 + (a*b*c)^0.5)
Parte trigonométrica [src] 
     _______________________
    /                 _____ 
   /  4 + a*b*c   4*\/ b*c  
  /   --------- + --------- 
\/        a           a     
----------------------------
             _______        
       2 + \/ a*b*c
4bca+abc+4aabc+2\frac{\sqrt{\frac{4 \sqrt{b c}}{a} + \frac{a b c + 4}{a}}}{\sqrt{a b c} + 2} 
sqrt((4 + a*b*c)/a + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Combinatoria [src] 
     _____________________
    /               _____ 
   /  4         4*\/ b*c  
  /   - + b*c + --------- 
\/    a             a     
--------------------------
            _______       
      2 + \/ a*b*c
bc+4bca+4aabc+2\frac{\sqrt{b c + \frac{4 \sqrt{b c}}{a} + \frac{4}{a}}}{\sqrt{a b c} + 2} 
sqrt(4/a + b*c + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Compilar la expresión [src] 
     _______________________
    /         _____         
   /  4 + 4*\/ b*c  + a*b*c 
  /   --------------------- 
\/              a           
----------------------------
             _______        
       2 + \/ a*b*c
abc+4bc+4aabc+2\frac{\sqrt{\frac{a b c + 4 \sqrt{b c} + 4}{a}}}{\sqrt{a b c} + 2} 
     _______________________
    /                 _____ 
   /  4 + a*b*c   4*\/ b*c  
  /   --------- + --------- 
\/        a           a     
----------------------------
             _______        
       2 + \/ a*b*c
4bca+abc+4aabc+2\frac{\sqrt{\frac{4 \sqrt{b c}}{a} + \frac{a b c + 4}{a}}}{\sqrt{a b c} + 2} 
sqrt((4 + a*b*c)/a + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Denominador común [src] 
     _____________________
    /               _____ 
   /  4         4*\/ b*c  
  /   - + b*c + --------- 
\/    a             a     
--------------------------
            _______       
      2 + \/ a*b*c
bc+4bca+4aabc+2\frac{\sqrt{b c + \frac{4 \sqrt{b c}}{a} + \frac{4}{a}}}{\sqrt{a b c} + 2} 
sqrt(4/a + b*c + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Abrimos la expresión [src] 
     ___________________________
    /                 ___   ___ 
   /  a*b*c + 4   4*\/ b *\/ c  
  /   --------- + ------------- 
\/        a             a       
--------------------------------
             ___   _____        
       2 + \/ c *\/ a*b
4bca+cab+4acab+2\frac{\sqrt{\frac{4 \sqrt{b} \sqrt{c}}{a} + \frac{c a b + 4}{a}}}{\sqrt{c} \sqrt{a b} + 2} 
     _______________________
    /                 _____ 
   /  a*b*c + 4     \/ b*c  
  /   --------- + 4*------- 
\/        a            a    
----------------------------
             _______        
       2 + \/ a*b*c
4bca+cab+4aabc+2\frac{\sqrt{4 \frac{\sqrt{b c}}{a} + \frac{c a b + 4}{a}}}{\sqrt{a b c} + 2} 
sqrt(((a*b)*c + 4)/a + 4*(sqrt(b*c)/a))/(2 + sqrt(a*b*c))
Denominador racional [src] 
     _____________________                 
    /               _____                  
   /  4         4*\/ b*c   /       _______\
  /   - + b*c + --------- *\-2 + \/ a*b*c /
\/    a             a                      
-------------------------------------------
                 -4 + a*b*c
(abc−2)bc+4bca+4aabc−4\frac{\left(\sqrt{a b c} - 2\right) \sqrt{b c + \frac{4 \sqrt{b c}}{a} + \frac{4}{a}}}{a b c - 4} 
sqrt(4/a + b*c + 4*sqrt(b*c)/a)*(-2 + sqrt(a*b*c))/(-4 + a*b*c)
Potencias [src] 
     _______________________
    /                 _____ 
   /  4 + a*b*c   4*\/ b*c  
  /   --------- + --------- 
\/        a           a     
----------------------------
             _______        
       2 + \/ a*b*c
4bca+abc+4aabc+2\frac{\sqrt{\frac{4 \sqrt{b c}}{a} + \frac{a b c + 4}{a}}}{\sqrt{a b c} + 2} 
sqrt((4 + a*b*c)/a + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Unión de expresiones racionales [src] 
     _______________________
    /         _____         
   /  4 + 4*\/ b*c  + a*b*c 
  /   --------------------- 
\/              a           
----------------------------
             _______        
       2 + \/ a*b*c
abc+4bc+4aabc+2\frac{\sqrt{\frac{a b c + 4 \sqrt{b c} + 4}{a}}}{\sqrt{a b c} + 2} 
sqrt((4 + 4*sqrt(b*c) + a*b*c)/a)/(2 + sqrt(a*b*c))
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