Simplificación general
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$$\frac{1}{x^{2} y^{2}}$$
(1/x + 1/y)*(x/(-y^2 + x*y) + y/(-x^2 + x*y))/(x^2 + y^2 + 2.0*x*y)
(1/x + 1/y)*(x/(-y^2 + x*y) + y/(-x^2 + x*y))/(x^2 + y^2 + 2.0*x*y)
Abrimos la expresión
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/1 1\ / y x \
|- + -|*|-------- + --------|
\x y/ | 2 2|
\x*y - x x*y - y /
-----------------------------
2 2
x + 2*x*y + y
$$\frac{\left(\frac{1}{y} + \frac{1}{x}\right) \left(\frac{x}{x y - y^{2}} + \frac{y}{- x^{2} + x y}\right)}{y^{2} + \left(x^{2} + 2 x y\right)}$$
(1/x + 1/y)*(y/(x*y - x^2) + x/(x*y - y^2))/(x^2 + (2*x)*y + y^2)
Denominador racional
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/ / 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/
$$\frac{\left(x + y\right) \left(x \left(- x^{2} + x y\right) + y \left(x y - y^{2}\right)\right)}{x y \left(- x^{2} + x y\right) \left(x y - y^{2}\right) \left(x^{2} + 2 x y + y^{2}\right)}$$
(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
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/1 1\ / x y \
|- + -|*|---------- + ----------|
\x y/ | 2 2 |
\- y + x*y - x + x*y/
---------------------------------
2 2
x + y + 2*x*y
$$\frac{\left(\frac{1}{y} + \frac{1}{x}\right) \left(\frac{x}{x y - y^{2}} + \frac{y}{- x^{2} + x y}\right)}{x^{2} + 2 x y + y^{2}}$$
(1/x + 1/y)*(x/(-y^2 + x*y) + y/(-x^2 + x*y))/(x^2 + y^2 + 2*x*y)
Unión de expresiones racionales
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/ 2 2 \
(x + y)*\x *(y - x) + y *(x - y)/
----------------------------------------
2 2 / 2 \
x *y *(x - y)*(y - x)*\y + x*(x + 2*y)/
$$\frac{\left(x + y\right) \left(x^{2} \left(- x + y\right) + y^{2} \left(x - y\right)\right)}{x^{2} y^{2} \left(- x + y\right) \left(x - y\right) \left(x \left(x + 2 y\right) + y^{2}\right)}$$
(x + y)*(x^2*(y - x) + y^2*(x - y))/(x^2*y^2*(x - y)*(y - x)*(y^2 + x*(x + 2*y)))
$$\frac{1}{x^{2} y^{2}}$$
Parte trigonométrica
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/1 1\ / x y \
|- + -|*|---------- + ----------|
\x y/ | 2 2 |
\- y + x*y - x + x*y/
---------------------------------
2 2
x + y + 2*x*y
$$\frac{\left(\frac{1}{y} + \frac{1}{x}\right) \left(\frac{x}{x y - y^{2}} + \frac{y}{- x^{2} + x y}\right)}{x^{2} + 2 x y + y^{2}}$$
(1/x + 1/y)*(x/(-y^2 + x*y) + y/(-x^2 + x*y))/(x^2 + y^2 + 2*x*y)
$$\frac{1}{x^{2} y^{2}}$$
/1 1\ / x y \
|- + -|*|---------- + ----------|
\x y/ | 2 2 |
\- y + x*y - x + x*y/
---------------------------------
2 2
x + y + 2*x*y
$$\frac{\left(\frac{1}{y} + \frac{1}{x}\right) \left(\frac{x}{x y - y^{2}} + \frac{y}{- x^{2} + x y}\right)}{x^{2} + 2 x y + y^{2}}$$
(1/x + 1/y)*(x/(-y^2 + x*y) + y/(-x^2 + x*y))/(x^2 + y^2 + 2*x*y)