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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    ___       ___                          
a*\/ a  + b*\/ b      ___                  
----------------- + \/ b                   
        ___                     ___        
      \/ a                  2*\/ b      ___
------------------------- + ------- + \/ b 
          a - b                ___         
                             \/ a
b+(b+aa+bbaa−b+2ba)\sqrt{b} + \left(\frac{\sqrt{b} + \frac{\sqrt{a} a + \sqrt{b} b}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}}\right) 
((a*sqrt(a) + b*sqrt(b))/sqrt(a) + sqrt(b))/(a - b) + (2*sqrt(b))/sqrt(a) + sqrt(b)
Simplificación general [src] 
 2       ___    2   ___      3/2     ___  3/2      3/2   ___
a  + a*\/ b  + a *\/ b  - a*b    - \/ a *b    + 2*a   *\/ b 
------------------------------------------------------------
                         a*(a - b)
2a32b−ab32+a2b+a2−ab32+aba(a−b)\frac{2 a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + a^{2} \sqrt{b} + a^{2} - a b^{\frac{3}{2}} + a \sqrt{b}}{a \left(a - b\right)} 
(a^2 + a*sqrt(b) + a^2*sqrt(b) - a*b^(3/2) - sqrt(a)*b^(3/2) + 2*a^(3/2)*sqrt(b))/(a*(a - b))
Parte trigonométrica [src] 
                 3/2    3/2          
          ___   a    + b             
        \/ b  + -----------          
                     ___          ___
  ___              \/ a       2*\/ b 
\/ b  + ------------------- + -------
               a - b             ___ 
                               \/ a
b+b+a32+b32aa−b+2ba\sqrt{b} + \frac{\sqrt{b} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}} 
sqrt(b) + (sqrt(b) + (a^(3/2) + b^(3/2))/sqrt(a))/(a - b) + 2*sqrt(b)/sqrt(a)
Compilar la expresión [src] 
                             3/2    3/2
                      ___   a    + b   
                    \/ b  + -----------
                                 ___   
  ___ /      2  \              \/ a    
\/ b *|1 + -----| + -------------------
      |      ___|          a - b       
      \    \/ a /
b(1+2a)+b+a32+b32aa−b\sqrt{b} \left(1 + \frac{2}{\sqrt{a}}\right) + \frac{\sqrt{b} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} 
                 3/2    3/2          
          ___   a    + b             
        \/ b  + -----------          
                     ___          ___
  ___              \/ a       2*\/ b 
\/ b  + ------------------- + -------
               a - b             ___ 
                               \/ a
b+b+a32+b32aa−b+2ba\sqrt{b} + \frac{\sqrt{b} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}} 
sqrt(b) + (sqrt(b) + (a^(3/2) + b^(3/2))/sqrt(a))/(a - b) + 2*sqrt(b)/sqrt(a)
Respuesta numérica [src] 
b^0.5 + (b^0.5 + a^(-0.5)*(a^1.5 + b^1.5))/(a - b) + 2.0*a^(-0.5)*b^0.5
b^0.5 + (b^0.5 + a^(-0.5)*(a^1.5 + b^1.5))/(a - b) + 2.0*a^(-0.5)*b^0.5
Denominador común [src] 
                      ___     ___  3/2      3/2   ___
      ___   a*b + a*\/ b  - \/ a *b    + 2*a   *\/ b 
1 + \/ b  + -----------------------------------------
                              2                      
                             a  - a*b
b+1+2a32b−ab32+ab+aba2−ab\sqrt{b} + 1 + \frac{2 a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + a \sqrt{b} + a b}{a^{2} - a b} 
1 + sqrt(b) + (a*b + a*sqrt(b) - sqrt(a)*b^(3/2) + 2*a^(3/2)*sqrt(b))/(a^2 - a*b)
Potencias [src] 
                 3/2    3/2          
          ___   a    + b             
        \/ b  + -----------          
                     ___          ___
  ___              \/ a       2*\/ b 
\/ b  + ------------------- + -------
               a - b             ___ 
                               \/ a
b+b+a32+b32aa−b+2ba\sqrt{b} + \frac{\sqrt{b} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}} 
sqrt(b) + (sqrt(b) + (a^(3/2) + b^(3/2))/sqrt(a))/(a - b) + 2*sqrt(b)/sqrt(a)
Denominador racional [src] 
  ___ / 3/2    3/2     ___   ___\       ___               ___   ___        
\/ a *\a    + b    + \/ a *\/ b / + a*\/ b *(a - b) + 2*\/ a *\/ b *(a - b)
---------------------------------------------------------------------------
                                 a*(a - b)
2ab(a−b)+a(a32+ab+b32)+ab(a−b)a(a−b)\frac{2 \sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \left(a^{\frac{3}{2}} + \sqrt{a} \sqrt{b} + b^{\frac{3}{2}}\right) + a \sqrt{b} \left(a - b\right)}{a \left(a - b\right)} 
(sqrt(a)*(a^(3/2) + b^(3/2) + sqrt(a)*sqrt(b)) + a*sqrt(b)*(a - b) + 2*sqrt(a)*sqrt(b)*(a - b))/(a*(a - b))
Unión de expresiones racionales [src] 
 3/2    3/2     ___   ___       ___             ___   ___        
a    + b    + \/ a *\/ b  + 2*\/ b *(a - b) + \/ a *\/ b *(a - b)
-----------------------------------------------------------------
                            ___                                  
                          \/ a *(a - b)
a32+ab(a−b)+ab+b32+2b(a−b)a(a−b)\frac{a^{\frac{3}{2}} + \sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \sqrt{b} + b^{\frac{3}{2}} + 2 \sqrt{b} \left(a - b\right)}{\sqrt{a} \left(a - b\right)} 
(a^(3/2) + b^(3/2) + sqrt(a)*sqrt(b) + 2*sqrt(b)*(a - b) + sqrt(a)*sqrt(b)*(a - b))/(sqrt(a)*(a - b))
Combinatoria [src] 
 3/2    3/2     ___   ___    3/2   ___     ___  3/2         ___
a    - b    + \/ a *\/ b  + a   *\/ b  - \/ a *b    + 2*a*\/ b 
---------------------------------------------------------------
                           ___                                 
                         \/ a *(a - b)
a32b+a32−ab32+ab+2ab−b32a(a−b)\frac{a^{\frac{3}{2}} \sqrt{b} + a^{\frac{3}{2}} - \sqrt{a} b^{\frac{3}{2}} + \sqrt{a} \sqrt{b} + 2 a \sqrt{b} - b^{\frac{3}{2}}}{\sqrt{a} \left(a - b\right)} 
(a^(3/2) - b^(3/2) + sqrt(a)*sqrt(b) + a^(3/2)*sqrt(b) - sqrt(a)*b^(3/2) + 2*a*sqrt(b))/(sqrt(a)*(a - b))
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