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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] 
              ___                          
    ___   b*\/ b      ___                  
a*\/ a  + ------- + \/ b                   
             ___                ___        
           \/ a             2*\/ b      ___
------------------------- + ------- + \/ b 
          a - b                ___         
                             \/ a
b+(b+(aa+bba)a−b+2ba)\sqrt{b} + \left(\frac{\sqrt{b} + \left(\sqrt{a} a + \frac{\sqrt{b} b}{\sqrt{a}}\right)}{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    3/2     ___   ___\       ___               ___   ___        
\/ a *\a  + b    + \/ a *\/ b / + a*\/ b *(a - b) + 2*\/ a *\/ b *(a - b)
-------------------------------------------------------------------------
                                a*(a - b)
2ab(a−b)+a(ab+a2+b32)+ab(a−b)a(a−b)\frac{2 \sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \left(\sqrt{a} \sqrt{b} + a^{2} + b^{\frac{3}{2}}\right) + a \sqrt{b} \left(a - b\right)}{a \left(a - b\right)} 
(sqrt(a)*(a^2 + b^(3/2) + sqrt(a)*sqrt(b)) + a*sqrt(b)*(a - b) + 2*sqrt(a)*sqrt(b)*(a - b))/(a*(a - b))
Respuesta numérica [src] 
b^0.5 + (a^1.5 + b^0.5 + a^(-0.5)*b^1.5)/(a - b) + 2.0*a^(-0.5)*b^0.5
b^0.5 + (a^1.5 + b^0.5 + a^(-0.5)*b^1.5)/(a - b) + 2.0*a^(-0.5)*b^0.5
Compilar la expresión [src] 
                                     3/2
                     3/2     ___    b   
                    a    + \/ b  + -----
                                     ___
  ___ /      2  \                  \/ a 
\/ b *|1 + -----| + --------------------
      |      ___|          a - b        
      \    \/ a /
b(1+2a)+a32+b+b32aa−b\sqrt{b} \left(1 + \frac{2}{\sqrt{a}}\right) + \frac{a^{\frac{3}{2}} + \sqrt{b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} 
                         3/2          
         3/2     ___    b             
        a    + \/ b  + -----          
                         ___       ___
  ___                  \/ a    2*\/ b 
\/ b  + -------------------- + -------
               a - b              ___ 
                                \/ a
b+a32+b+b32aa−b+2ba\sqrt{b} + \frac{a^{\frac{3}{2}} + \sqrt{b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}} 
sqrt(b) + (a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a))/(a - b) + 2*sqrt(b)/sqrt(a)
Potencias [src] 
                         3/2          
         3/2     ___    b             
        a    + \/ b  + -----          
                         ___       ___
  ___                  \/ a    2*\/ b 
\/ b  + -------------------- + -------
               a - b              ___ 
                                \/ a
b+a32+b+b32aa−b+2ba\sqrt{b} + \frac{a^{\frac{3}{2}} + \sqrt{b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}} 
sqrt(b) + (a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a))/(a - b) + 2*sqrt(b)/sqrt(a)
Unión de expresiones racionales [src] 
 2    3/2     ___   ___       ___             ___   ___        
a  + b    + \/ a *\/ b  + 2*\/ b *(a - b) + \/ a *\/ b *(a - b)
---------------------------------------------------------------
                           ___                                 
                         \/ a *(a - b)
ab(a−b)+ab+a2+b32+2b(a−b)a(a−b)\frac{\sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \sqrt{b} + a^{2} + b^{\frac{3}{2}} + 2 \sqrt{b} \left(a - b\right)}{\sqrt{a} \left(a - b\right)} 
(a^2 + b^(3/2) + sqrt(a)*sqrt(b) + 2*sqrt(b)*(a - b) + sqrt(a)*sqrt(b)*(a - b))/(sqrt(a)*(a - b))
Parte trigonométrica [src] 
                         3/2          
         3/2     ___    b             
        a    + \/ b  + -----          
                         ___       ___
  ___                  \/ a    2*\/ b 
\/ b  + -------------------- + -------
               a - b              ___ 
                                \/ a
b+a32+b+b32aa−b+2ba\sqrt{b} + \frac{a^{\frac{3}{2}} + \sqrt{b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}} 
sqrt(b) + (a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a))/(a - b) + 2*sqrt(b)/sqrt(a)
Denominador racional [src] 
  ___ / 2    3/2     ___   ___\       ___               ___   ___        
\/ a *\a  + b    + \/ a *\/ b / + a*\/ b *(a - b) + 2*\/ a *\/ b *(a - b)
-------------------------------------------------------------------------
                                a*(a - b)
2ab(a−b)+a(ab+a2+b32)+ab(a−b)a(a−b)\frac{2 \sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \left(\sqrt{a} \sqrt{b} + a^{2} + b^{\frac{3}{2}}\right) + a \sqrt{b} \left(a - b\right)}{a \left(a - b\right)} 
(sqrt(a)*(a^2 + b^(3/2) + sqrt(a)*sqrt(b)) + a*sqrt(b)*(a - b) + 2*sqrt(a)*sqrt(b)*(a - b))/(a*(a - b))
Denominador común [src] 
         5/2       ___     ___  3/2      3/2   ___
  ___   a    + a*\/ b  - \/ a *b    + 2*a   *\/ b 
\/ b  + ------------------------------------------
                          2                       
                         a  - a*b
b+a52+2a32b−ab32+aba2−ab\sqrt{b} + \frac{a^{\frac{5}{2}} + 2 a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + a \sqrt{b}}{a^{2} - a b} 
sqrt(b) + (a^(5/2) + a*sqrt(b) - sqrt(a)*b^(3/2) + 2*a^(3/2)*sqrt(b))/(a^2 - a*b)
Combinatoria [src] 
 2    3/2     ___   ___    3/2   ___     ___  3/2         ___
a  - b    + \/ a *\/ b  + a   *\/ b  - \/ a *b    + 2*a*\/ b 
-------------------------------------------------------------
                          ___                                
                        \/ a *(a - b)
a32b−ab32+ab+a2+2ab−b32a(a−b)\frac{a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + \sqrt{a} \sqrt{b} + a^{2} + 2 a \sqrt{b} - b^{\frac{3}{2}}}{\sqrt{a} \left(a - b\right)} 
(a^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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