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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 |                
|-----------------|                
|    ___     ___  |          ___   
\  \/ a  + \/ b   /      2*\/ b    
------------------- + -------------
       a - b            ___     ___
                      \/ a  + \/ b
2ba+b+1a+b(aa+bb)a−b\frac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{\frac{1}{\sqrt{a} + \sqrt{b}} \left(\sqrt{a} a + \sqrt{b} b\right)}{a - b} 
((a*sqrt(a) + b*sqrt(b))/(sqrt(a) + sqrt(b)))/(a - b) + (2*sqrt(b))/(sqrt(a) + sqrt(b))
Simplificación general [src] 
 3/2    3/2       ___        
a    + b    + 2*\/ b *(a - b)
-----------------------------
           /  ___     ___\   
   (a - b)*\\/ a  + \/ b /
a32+b32+2b(a−b)(a+b)(a−b)\frac{a^{\frac{3}{2}} + b^{\frac{3}{2}} + 2 \sqrt{b} \left(a - b\right)}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)} 
(a^(3/2) + b^(3/2) + 2*sqrt(b)*(a - b))/((a - b)*(sqrt(a) + sqrt(b)))
Parte trigonométrica [src] 
       ___             3/2    3/2      
   2*\/ b             a    + b         
------------- + -----------------------
  ___     ___           /  ___     ___\
\/ a  + \/ b    (a - b)*\\/ a  + \/ b /
2ba+b+a32+b32(a+b)(a−b)\frac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)} 
2*sqrt(b)/(sqrt(a) + sqrt(b)) + (a^(3/2) + b^(3/2))/((a - b)*(sqrt(a) + sqrt(b)))
Compilar la expresión [src] 
       ___             3/2    3/2      
   2*\/ b             a    + b         
------------- + -----------------------
  ___     ___           /  ___     ___\
\/ a  + \/ b    (a - b)*\\/ a  + \/ b /
2ba+b+a32+b32(a+b)(a−b)\frac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)} 
2*sqrt(b)/(sqrt(a) + sqrt(b)) + (a^(3/2) + b^(3/2))/((a - b)*(sqrt(a) + sqrt(b)))
Combinatoria [src] 
 3/2    3/2         ___
a    - b    + 2*a*\/ b 
-----------------------
        /  ___     ___\
(a - b)*\\/ a  + \/ b /
a32+2ab−b32(a+b)(a−b)\frac{a^{\frac{3}{2}} + 2 a \sqrt{b} - b^{\frac{3}{2}}}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)} 
(a^(3/2) - b^(3/2) + 2*a*sqrt(b))/((a - b)*(sqrt(a) + sqrt(b)))
Denominador racional [src] 
                  2                     2                             2                        2                               2
 2 /  ___     ___\     2 /  ___     ___\      ___  3/2 /  ___     ___\          /  ___     ___\       3/2   ___ /  ___     ___\ 
a *\\/ a  - \/ b /  - b *\\/ a  - \/ b /  - \/ a *b   *\\/ a  - \/ b /  + 2*a*b*\\/ a  - \/ b /  + 3*a   *\/ b *\\/ a  - \/ b / 
--------------------------------------------------------------------------------------------------------------------------------
                                                                   3                                                            
                                                            (a - b)
3a32b(a−b)2−ab32(a−b)2+a2(a−b)2+2ab(a−b)2−b2(a−b)2(a−b)3\frac{3 a^{\frac{3}{2}} \sqrt{b} \left(\sqrt{a} - \sqrt{b}\right)^{2} - \sqrt{a} b^{\frac{3}{2}} \left(\sqrt{a} - \sqrt{b}\right)^{2} + a^{2} \left(\sqrt{a} - \sqrt{b}\right)^{2} + 2 a b \left(\sqrt{a} - \sqrt{b}\right)^{2} - b^{2} \left(\sqrt{a} - \sqrt{b}\right)^{2}}{\left(a - b\right)^{3}} 
(a^2*(sqrt(a) - sqrt(b))^2 - b^2*(sqrt(a) - sqrt(b))^2 - sqrt(a)*b^(3/2)*(sqrt(a) - sqrt(b))^2 + 2*a*b*(sqrt(a) - sqrt(b))^2 + 3*a^(3/2)*sqrt(b)*(sqrt(a) - sqrt(b))^2)/(a - b)^3
Denominador común [src] 
         3/2    3/2         ___    
        b    - a    + 2*b*\/ a     
2 + -------------------------------
     3/2    3/2       ___       ___
    a    - b    + a*\/ b  - b*\/ a
−a32+2ab+b32a32−ab+ab−b32+2\frac{- a^{\frac{3}{2}} + 2 \sqrt{a} b + b^{\frac{3}{2}}}{a^{\frac{3}{2}} - \sqrt{a} b + a \sqrt{b} - b^{\frac{3}{2}}} + 2 
2 + (b^(3/2) - a^(3/2) + 2*b*sqrt(a))/(a^(3/2) - b^(3/2) + a*sqrt(b) - b*sqrt(a))
Unión de expresiones racionales [src] 
 3/2    3/2       ___        
a    + b    + 2*\/ b *(a - b)
-----------------------------
           /  ___     ___\   
   (a - b)*\\/ a  + \/ b /
a32+b32+2b(a−b)(a+b)(a−b)\frac{a^{\frac{3}{2}} + b^{\frac{3}{2}} + 2 \sqrt{b} \left(a - b\right)}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)} 
(a^(3/2) + b^(3/2) + 2*sqrt(b)*(a - b))/((a - b)*(sqrt(a) + sqrt(b)))
Potencias [src] 
       ___             3/2    3/2      
   2*\/ b             a    + b         
------------- + -----------------------
  ___     ___           /  ___     ___\
\/ a  + \/ b    (a - b)*\\/ a  + \/ b /
2ba+b+a32+b32(a+b)(a−b)\frac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)} 
2*sqrt(b)/(sqrt(a) + sqrt(b)) + (a^(3/2) + b^(3/2))/((a - b)*(sqrt(a) + sqrt(b)))
Respuesta numérica [src] 
2.0*b^0.5/(a^0.5 + b^0.5) + (a^1.5 + b^1.5)/((a - b)*(a^0.5 + b^0.5))
2.0*b^0.5/(a^0.5 + b^0.5) + (a^1.5 + b^1.5)/((a - b)*(a^0.5 + b^0.5))
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