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Simplificación de expresiones/ Descomposición en fracciones simples/ ((x^3+y^3)/(x+y))/(x^2-y^2)+(2*y)/(x+y)-(x*y)/(x^2-y^2)

¿Cómo vas a descomponer esta ((x^3+y^3)/(x+y))/(x^2-y^2)+(2*y)/(x+y)-(x*y)/(x^2-y^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
/ 3    3\                  
|x  + y |                  
|-------|                  
\ x + y /    2*y      x*y  
--------- + ----- - -------
  2    2    x + y    2    2
 x  - y             x  - y
−xyx2−y2+(2yx+y+1x+y(x3+y3)x2−y2)- \frac{x y}{x^{2} - y^{2}} + \left(\frac{2 y}{x + y} + \frac{\frac{1}{x + y} \left(x^{3} + y^{3}\right)}{x^{2} - y^{2}}\right) 
((x^3 + y^3)/(x + y))/(x^2 - y^2) + (2*y)/(x + y) - x*y/(x^2 - y^2)
Descomposición de una fracción [src] 
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Simplificación general [src] 
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Respuesta numérica [src] 
2.0*y/(x + y) + (x^3 + y^3)/((x + y)*(x^2 - y^2)) - x*y/(x^2 - y^2)
2.0*y/(x + y) + (x^3 + y^3)/((x + y)*(x^2 - y^2)) - x*y/(x^2 - y^2)
Unión de expresiones racionales [src] 
 3    3       / 2    2\              
x  + y  + 2*y*\x  - y / - x*y*(x + y)
-------------------------------------
                  / 2    2\          
          (x + y)*\x  - y /
x3−xy(x+y)+y3+2y(x2−y2)(x+y)(x2−y2)\frac{x^{3} - x y \left(x + y\right) + y^{3} + 2 y \left(x^{2} - y^{2}\right)}{\left(x + y\right) \left(x^{2} - y^{2}\right)} 
(x^3 + y^3 + 2*y*(x^2 - y^2) - x*y*(x + y))/((x + y)*(x^2 - y^2))
Combinatoria [src] 
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Denominador racional [src] 
/ 2    2\ /        / 3    3\               / 2    2\\              2 / 2    2\
\x  - y /*\(x + y)*\x  + y / + 2*y*(x + y)*\x  - y // - x*y*(x + y) *\x  - y /
------------------------------------------------------------------------------
                                               2                              
                                    2 / 2    2\                               
                             (x + y) *\x  - y /
−xy(x+y)2(x2−y2)+(x2−y2)(2y(x+y)(x2−y2)+(x+y)(x3+y3))(x+y)2(x2−y2)2\frac{- x y \left(x + y\right)^{2} \left(x^{2} - y^{2}\right) + \left(x^{2} - y^{2}\right) \left(2 y \left(x + y\right) \left(x^{2} - y^{2}\right) + \left(x + y\right) \left(x^{3} + y^{3}\right)\right)}{\left(x + y\right)^{2} \left(x^{2} - y^{2}\right)^{2}} 
((x^2 - y^2)*((x + y)*(x^3 + y^3) + 2*y*(x + y)*(x^2 - y^2)) - x*y*(x + y)^2*(x^2 - y^2))/((x + y)^2*(x^2 - y^2)^2)
Denominador común [src] 
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Compilar la expresión [src] 
              3    3               
 2*y         x  + y           x*y  
----- + ----------------- - -------
x + y           / 2    2\    2    2
        (x + y)*\x  - y /   x  - y
−xyx2−y2+2yx+y+x3+y3(x+y)(x2−y2)- \frac{x y}{x^{2} - y^{2}} + \frac{2 y}{x + y} + \frac{x^{3} + y^{3}}{\left(x + y\right) \left(x^{2} - y^{2}\right)} 
                            3    3     
  /  2        x   \        x  + y      
y*|----- - -------| + -----------------
  |x + y    2    2|           / 2    2\
  \        x  - y /   (x + y)*\x  - y /
y(−xx2−y2+2x+y)+x3+y3(x+y)(x2−y2)y \left(- \frac{x}{x^{2} - y^{2}} + \frac{2}{x + y}\right) + \frac{x^{3} + y^{3}}{\left(x + y\right) \left(x^{2} - y^{2}\right)} 
y*(2/(x + y) - x/(x^2 - y^2)) + (x^3 + y^3)/((x + y)*(x^2 - y^2))
Potencias [src] 
              3    3               
 2*y         x  + y           x*y  
----- + ----------------- - -------
x + y           / 2    2\    2    2
        (x + y)*\x  - y /   x  - y
−xyx2−y2+2yx+y+x3+y3(x+y)(x2−y2)- \frac{x y}{x^{2} - y^{2}} + \frac{2 y}{x + y} + \frac{x^{3} + y^{3}}{\left(x + y\right) \left(x^{2} - y^{2}\right)} 
2*y/(x + y) + (x^3 + y^3)/((x + y)*(x^2 - y^2)) - x*y/(x^2 - y^2)
Parte trigonométrica [src] 
              3    3               
 2*y         x  + y           x*y  
----- + ----------------- - -------
x + y           / 2    2\    2    2
        (x + y)*\x  - y /   x  - y
−xyx2−y2+2yx+y+x3+y3(x+y)(x2−y2)- \frac{x y}{x^{2} - y^{2}} + \frac{2 y}{x + y} + \frac{x^{3} + y^{3}}{\left(x + y\right) \left(x^{2} - y^{2}\right)} 
2*y/(x + y) + (x^3 + y^3)/((x + y)*(x^2 - y^2)) - x*y/(x^2 - y^2)
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