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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    \/ b    2*\/ b      ___
a*\/ a  + ------- + ----- + ------- + \/ b 
             ___    a - b      ___         
           \/ a              \/ a
b+((ba−b+(aa+bba))+2ba)\sqrt{b} + \left(\left(\frac{\sqrt{b}}{a - b} + \left(\sqrt{a} a + \frac{\sqrt{b} b}{\sqrt{a}}\right)\right) + \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] 
  ___   ___     ___         / 3/2     ___\     ___                
\/ a *\/ b  + \/ a *(a - b)*\a    + \/ b / + \/ b *(2 + b)*(a - b)
------------------------------------------------------------------
                            ___                                   
                          \/ a *(a - b)
ab+a(a−b)(a32+b)+b(a−b)(b+2)a(a−b)\frac{\sqrt{a} \sqrt{b} + \sqrt{a} \left(a - b\right) \left(a^{\frac{3}{2}} + \sqrt{b}\right) + \sqrt{b} \left(a - b\right) \left(b + 2\right)}{\sqrt{a} \left(a - b\right)} 
(sqrt(a)*sqrt(b) + sqrt(a)*(a - b)*(a^(3/2) + sqrt(b)) + sqrt(b)*(2 + b)*(a - b))/(sqrt(a)*(a - b))
Respuesta numérica [src] 
a^1.5 + b^0.5 + a^(-0.5)*b^1.5 + b^0.5/(a - b) + 2.0*a^(-0.5)*b^0.5
a^1.5 + b^0.5 + a^(-0.5)*b^1.5 + b^0.5/(a - b) + 2.0*a^(-0.5)*b^0.5
Denominador común [src] 
 / 3    5/2      3/2      3/2     ___   ___    3/2   ___      2     ___  3/2         ___\ 
-\a  - b    - 2*b    + a*b    + \/ a *\/ b  + a   *\/ b  - b*a  - \/ a *b    + 2*a*\/ b / 
------------------------------------------------------------------------------------------
                                        3/2       ___                                     
                                     - a    + b*\/ a
−a32b−ab32+ab+a3−a2b+ab32+2ab−b52−2b32−a32+ab- \frac{a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + \sqrt{a} \sqrt{b} + a^{3} - a^{2} b + a b^{\frac{3}{2}} + 2 a \sqrt{b} - b^{\frac{5}{2}} - 2 b^{\frac{3}{2}}}{- a^{\frac{3}{2}} + \sqrt{a} b} 
-(a^3 - b^(5/2) - 2*b^(3/2) + a*b^(3/2) + sqrt(a)*sqrt(b) + a^(3/2)*sqrt(b) - b*a^2 - sqrt(a)*b^(3/2) + 2*a*sqrt(b))/(-a^(3/2) + b*sqrt(a))
Compilar la expresión [src] 
         3/2                            
 3/2    b        ___ /      1       2  \
a    + ----- + \/ b *|1 + ----- + -----|
         ___         |    a - b     ___|
       \/ a          \            \/ a /
a32+b(1+1a−b+2a)+b32aa^{\frac{3}{2}} + \sqrt{b} \left(1 + \frac{1}{a - b} + \frac{2}{\sqrt{a}}\right) + \frac{b^{\frac{3}{2}}}{\sqrt{a}} 
                 3/2     ___       ___
 3/2     ___    b      \/ b    2*\/ b 
a    + \/ b  + ----- + ----- + -------
                 ___   a - b      ___ 
               \/ a             \/ a
a32+b+ba−b+b32a+2baa^{\frac{3}{2}} + \sqrt{b} + \frac{\sqrt{b}}{a - b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}} + \frac{2 \sqrt{b}}{\sqrt{a}} 
                3/2       ___     ___
 3/2     ___   b    + 2*\/ b    \/ b 
a    + \/ b  + -------------- + -----
                     ___        a - b
                   \/ a
a32+b+ba−b+b32+2baa^{\frac{3}{2}} + \sqrt{b} + \frac{\sqrt{b}}{a - b} + \frac{b^{\frac{3}{2}} + 2 \sqrt{b}}{\sqrt{a}} 
a^(3/2) + sqrt(b) + (b^(3/2) + 2*sqrt(b))/sqrt(a) + sqrt(b)/(a - b)
Potencias [src] 
                 3/2     ___       ___
 3/2     ___    b      \/ b    2*\/ b 
a    + \/ b  + ----- + ----- + -------
                 ___   a - b      ___ 
               \/ a             \/ a
a32+b+ba−b+b32a+2baa^{\frac{3}{2}} + \sqrt{b} + \frac{\sqrt{b}}{a - b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}} + \frac{2 \sqrt{b}}{\sqrt{a}} 
a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a) + sqrt(b)/(a - b) + 2*sqrt(b)/sqrt(a)
Unión de expresiones racionales [src] 
  ___   ___           / 2    3/2\       ___             ___   ___        
\/ a *\/ b  + (a - b)*\a  + b   / + 2*\/ b *(a - b) + \/ a *\/ b *(a - b)
-------------------------------------------------------------------------
                                ___                                      
                              \/ a *(a - b)
ab(a−b)+ab+2b(a−b)+(a−b)(a2+b32)a(a−b)\frac{\sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \sqrt{b} + 2 \sqrt{b} \left(a - b\right) + \left(a - b\right) \left(a^{2} + b^{\frac{3}{2}}\right)}{\sqrt{a} \left(a - b\right)} 
(sqrt(a)*sqrt(b) + (a - b)*(a^2 + b^(3/2)) + 2*sqrt(b)*(a - b) + sqrt(a)*sqrt(b)*(a - b))/(sqrt(a)*(a - b))
Denominador racional [src] 
  ___ /  ___   ___           / 2    3/2\\       ___               ___   ___        
\/ a *\\/ a *\/ b  + (a - b)*\a  + b   // + a*\/ b *(a - b) + 2*\/ a *\/ b *(a - b)
-----------------------------------------------------------------------------------
                                     a*(a - b)
2ab(a−b)+a(ab+(a−b)(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} + \left(a - b\right) \left(a^{2} + b^{\frac{3}{2}}\right)\right) + a \sqrt{b} \left(a - b\right)}{a \left(a - b\right)} 
(sqrt(a)*(sqrt(a)*sqrt(b) + (a - b)*(a^2 + b^(3/2))) + a*sqrt(b)*(a - b) + 2*sqrt(a)*sqrt(b)*(a - b))/(a*(a - b))
Parte trigonométrica [src] 
                 3/2     ___       ___
 3/2     ___    b      \/ b    2*\/ b 
a    + \/ b  + ----- + ----- + -------
                 ___   a - b      ___ 
               \/ a             \/ a
a32+b+ba−b+b32a+2baa^{\frac{3}{2}} + \sqrt{b} + \frac{\sqrt{b}}{a - b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}} + \frac{2 \sqrt{b}}{\sqrt{a}} 
a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a) + sqrt(b)/(a - b) + 2*sqrt(b)/sqrt(a)
Combinatoria [src] 
 3    5/2      3/2      3/2     ___   ___    3/2   ___      2     ___  3/2         ___
a  - b    - 2*b    + a*b    + \/ a *\/ b  + a   *\/ b  - b*a  - \/ a *b    + 2*a*\/ b 
--------------------------------------------------------------------------------------
                                      ___                                             
                                    \/ a *(a - b)
a32b−ab32+ab+a3−a2b+ab32+2ab−b52−2b32a(a−b)\frac{a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + \sqrt{a} \sqrt{b} + a^{3} - a^{2} b + a b^{\frac{3}{2}} + 2 a \sqrt{b} - b^{\frac{5}{2}} - 2 b^{\frac{3}{2}}}{\sqrt{a} \left(a - b\right)} 
(a^3 - b^(5/2) - 2*b^(3/2) + a*b^(3/2) + sqrt(a)*sqrt(b) + a^(3/2)*sqrt(b) - b*a^2 - sqrt(a)*b^(3/2) + 2*a*sqrt(b))/(sqrt(a)*(a - b))
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