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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
$$\frac{\sqrt{4 \sqrt{\frac{b c}{a}} + \frac{c a b + 4}{a}}}{\sqrt{c a b} + 2}$$ 
sqrt(((a*b)*c + 4)/a + 4*sqrt((b*c)/a))/(sqrt((a*b)*c) + 2)
Simplificación general [src] 
     _______________________
    /           _____       
   /  4        / b*c        
  /   - + 4*  /  ---  + b*c 
\/    a     \/    a         
----------------------------
             _______        
       2 + \/ a*b*c
$$\frac{\sqrt{b c + 4 \sqrt{\frac{b c}{a}} + \frac{4}{a}}}{\sqrt{a b c} + 2}$$ 
sqrt(4/a + 4*sqrt(b*c/a) + b*c)/(2 + sqrt(a*b*c))
Potencias [src] 
     _________________________
    /       _____             
   /       / b*c    4 + a*b*c 
  /   4*  /  ---  + --------- 
\/      \/    a         a     
------------------------------
              _______         
        2 + \/ a*b*c
$$\frac{\sqrt{4 \sqrt{\frac{b c}{a}} + \frac{a b c + 4}{a}}}{\sqrt{a b c} + 2}$$ 
sqrt(4*sqrt(b*c/a) + (4 + a*b*c)/a)/(2 + sqrt(a*b*c))
Compilar la expresión [src] 
     _________________________
    /       _____             
   /       / b*c    4 + a*b*c 
  /   4*  /  ---  + --------- 
\/      \/    a         a     
------------------------------
              _______         
        2 + \/ a*b*c
$$\frac{\sqrt{4 \sqrt{\frac{b c}{a}} + \frac{a b c + 4}{a}}}{\sqrt{a b c} + 2}$$ 
sqrt(4*sqrt(b*c/a) + (4 + a*b*c)/a)/(2 + sqrt(a*b*c))
Abrimos la expresión [src] 
     _________________________
    /       _____             
   /       / b*c    a*b*c + 4 
  /   4*  /  ---  + --------- 
\/      \/    a         a     
------------------------------
              _______         
        2 + \/ a*b*c
$$\frac{\sqrt{4 \sqrt{\frac{b c}{a}} + \frac{c a b + 4}{a}}}{\sqrt{a b c} + 2}$$ 
     _______________________________
    /                   ___         
   /  a*b*c + 4        / 1    _____ 
  /   --------- + 4*  /  - *\/ b*c  
\/        a         \/   a          
------------------------------------
               ___   _____          
         2 + \/ c *\/ a*b
$$\frac{\sqrt{4 \sqrt{b c} \sqrt{\frac{1}{a}} + \frac{c a b + 4}{a}}}{\sqrt{c} \sqrt{a b} + 2}$$ 
sqrt(((a*b)*c + 4)/a + 4*sqrt(1/a)*sqrt(b*c))/(2 + sqrt(c)*sqrt(a*b))
Parte trigonométrica [src] 
     _________________________
    /       _____             
   /       / b*c    4 + a*b*c 
  /   4*  /  ---  + --------- 
\/      \/    a         a     
------------------------------
              _______         
        2 + \/ a*b*c
$$\frac{\sqrt{4 \sqrt{\frac{b c}{a}} + \frac{a b c + 4}{a}}}{\sqrt{a b c} + 2}$$ 
sqrt(4*sqrt(b*c/a) + (4 + a*b*c)/a)/(2 + sqrt(a*b*c))
Denominador común [src] 
     _______________________
    /           _____       
   /  4        / b*c        
  /   - + 4*  /  ---  + b*c 
\/    a     \/    a         
----------------------------
             _______        
       2 + \/ a*b*c
$$\frac{\sqrt{b c + 4 \sqrt{\frac{b c}{a}} + \frac{4}{a}}}{\sqrt{a b c} + 2}$$ 
sqrt(4/a + 4*sqrt(b*c/a) + b*c)/(2 + sqrt(a*b*c))
Denominador racional [src] 
     _______________________                 
    /           _____                        
   /  4        / b*c         /       _______\
  /   - + 4*  /  ---  + b*c *\-2 + \/ a*b*c /
\/    a     \/    a                          
---------------------------------------------
                  -4 + a*b*c
$$\frac{\left(\sqrt{a b c} - 2\right) \sqrt{b c + 4 \sqrt{\frac{b c}{a}} + \frac{4}{a}}}{a b c - 4}$$ 
sqrt(4/a + 4*sqrt(b*c/a) + b*c)*(-2 + sqrt(a*b*c))/(-4 + a*b*c)
Unión de expresiones racionales [src] 
       ___________________________
      /             _____         
     /             / b*c          
    /   4 + 4*a*  /  ---  + a*b*c 
   /            \/    a           
  /     ------------------------- 
\/                  a             
----------------------------------
                _______           
          2 + \/ a*b*c
$$\frac{\sqrt{\frac{a b c + 4 a \sqrt{\frac{b c}{a}} + 4}{a}}}{\sqrt{a b c} + 2}$$ 
sqrt((4 + 4*a*sqrt(b*c/a) + a*b*c)/a)/(2 + sqrt(a*b*c))
Respuesta numérica [src] 
2.0*((b*c/a)^0.5 + 0.25*(4.0 + a*b*c)/a)^0.5/(2.0 + (a*b*c)^0.5)
2.0*((b*c/a)^0.5 + 0.25*(4.0 + a*b*c)/a)^0.5/(2.0 + (a*b*c)^0.5)
Combinatoria [src] 
     _______________________
    /           _____       
   /  4        / b*c        
  /   - + 4*  /  ---  + b*c 
\/    a     \/    a         
----------------------------
             _______        
       2 + \/ a*b*c
$$\frac{\sqrt{b c + 4 \sqrt{\frac{b c}{a}} + \frac{4}{a}}}{\sqrt{a b c} + 2}$$ 
sqrt(4/a + 4*sqrt(b*c/a) + b*c)/(2 + sqrt(a*b*c))
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