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Simplificación de expresiones/ Descomposición en fracciones simples/ (y/(x*y-x^2)+x/(x*y-y^2))/(x^2+2*x*y+y^2)/(1/x+1/y)

¿Cómo vas a descomponer esta (y/(x*y-x^2)+x/(x*y-y^2))/(x^2+2*x*y+y^2)/(1/x+1/y) expresión en fracciones?

Expresión a simplificar:

Solución

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