3) Упростить: \(\frac{x}{2x-2y}+\frac{x}{2x+2y}\).

Вынесем 2 за скобки в знаменателях:

\[\frac{x}{2(x-y)}+\frac{x}{2(x+y)}.\]

Общий знаменатель: \(2(x-y)(x+y)\).

\[\frac{x(x+y)+x(x-y)}{2(x-y)(x+y)}=\frac{x[(x+y)+(x-y)]}{2(x-y)(x+y)}.\]

\[\frac{x\cdot2x}{2(x-y)(x+y)}=\frac{x^2}{(x-y)(x+y)}=\frac{x^2}{x^2-y^2}.\]

Ограничения: \(x\ne y\), \(x\ne -y\).

Ответ: \(\frac{x^2}{x^2-y^2}\), \(x\ne y\), \(x\ne -y\).