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Simplificación de expresiones/ Descomposición en fracciones simples/ Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+(b+2))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    _____________________
   /            ________ 
  /            /  2      
\/   2*b + 2*\/  b  - 4  
-------------------------
      ________           
     /  2                
   \/  b  - 4  + b + 2
$$\frac{\sqrt{2 b + 2 \sqrt{b^{2} - 4}}}{\left(b + 2\right) + \sqrt{b^{2} - 4}}$$ 
sqrt(2*b + 2*sqrt(b^2 - 4))/(sqrt(b^2 - 4) + b + 2)
Simplificación general [src] 
    ______________________
   /            _________ 
  /            /       2  
\/   2*b + 2*\/  -4 + b   
--------------------------
              _________   
             /       2    
   2 + b + \/  -4 + b
$$\frac{\sqrt{2 b + 2 \sqrt{b^{2} - 4}}}{b + \sqrt{b^{2} - 4} + 2}$$ 
sqrt(2*b + 2*sqrt(-4 + b^2))/(2 + b + sqrt(-4 + b^2))
Respuesta numérica [src] 
2.0*((-1 + 0.25*b^2)^0.5 + 0.5*b)^0.5/(2.0 + b + 2.0*(-1 + 0.25*b^2)^0.5)
2.0*((-1 + 0.25*b^2)^0.5 + 0.5*b)^0.5/(2.0 + b + 2.0*(-1 + 0.25*b^2)^0.5)
Denominador racional [src] 
    ______________________                       
   /            _________  /           _________\
  /            /       2   |          /       2 |
\/   2*b + 2*\/  -4 + b   *\2 + b - \/  -4 + b  /
-------------------------------------------------
                     8 + 4*b
$$\frac{\sqrt{2 b + 2 \sqrt{b^{2} - 4}} \left(b - \sqrt{b^{2} - 4} + 2\right)}{4 b + 8}$$ 
sqrt(2*b + 2*sqrt(-4 + b^2))*(2 + b - sqrt(-4 + b^2))/(8 + 4*b)
Combinatoria [src] 
          __________________
         /        _________ 
  ___   /        /       2  
\/ 2 *\/   b + \/  -4 + b   
----------------------------
               _________    
              /       2     
    2 + b + \/  -4 + b
$$\frac{\sqrt{2} \sqrt{b + \sqrt{b^{2} - 4}}}{b + \sqrt{b^{2} - 4} + 2}$$ 
sqrt(2)*sqrt(b + sqrt(-4 + b^2))/(2 + b + sqrt(-4 + b^2))
Compilar la expresión [src] 
    ______________________
   /            _________ 
  /            /       2  
\/   2*b + 2*\/  -4 + b   
--------------------------
              _________   
             /       2    
   2 + b + \/  -4 + b
$$\frac{\sqrt{2 b + 2 \sqrt{b^{2} - 4}}}{b + \sqrt{b^{2} - 4} + 2}$$ 
sqrt(2*b + 2*sqrt(-4 + b^2))/(2 + b + sqrt(-4 + b^2))
Parte trigonométrica [src] 
    ______________________
   /            _________ 
  /            /       2  
\/   2*b + 2*\/  -4 + b   
--------------------------
              _________   
             /       2    
   2 + b + \/  -4 + b
$$\frac{\sqrt{2 b + 2 \sqrt{b^{2} - 4}}}{b + \sqrt{b^{2} - 4} + 2}$$ 
sqrt(2*b + 2*sqrt(-4 + b^2))/(2 + b + sqrt(-4 + b^2))
Potencias [src] 
    ______________________
   /            _________ 
  /            /       2  
\/   2*b + 2*\/  -4 + b   
--------------------------
              _________   
             /       2    
   2 + b + \/  -4 + b
$$\frac{\sqrt{2 b + 2 \sqrt{b^{2} - 4}}}{b + \sqrt{b^{2} - 4} + 2}$$ 
sqrt(2*b + 2*sqrt(-4 + b^2))/(2 + b + sqrt(-4 + b^2))
Denominador común [src] 
          __________________
         /        _________ 
  ___   /        /       2  
\/ 2 *\/   b + \/  -4 + b   
----------------------------
               _________    
              /       2     
    2 + b + \/  -4 + b
$$\frac{\sqrt{2} \sqrt{b + \sqrt{b^{2} - 4}}}{b + \sqrt{b^{2} - 4} + 2}$$ 
sqrt(2)*sqrt(b + sqrt(-4 + b^2))/(2 + b + sqrt(-4 + b^2))
Unión de expresiones racionales [src] 
          __________________
         /        _________ 
  ___   /        /       2  
\/ 2 *\/   b + \/  -4 + b   
----------------------------
               _________    
              /       2     
    2 + b + \/  -4 + b
$$\frac{\sqrt{2} \sqrt{b + \sqrt{b^{2} - 4}}}{b + \sqrt{b^{2} - 4} + 2}$$ 
sqrt(2)*sqrt(b + sqrt(-4 + b^2))/(2 + b + sqrt(-4 + b^2))
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