7. 1) \(\frac{2x}{9-x^2}-\frac{1}{2x-6}\); 3) \(\frac{2}{4c^2-25}+\frac{3c}{15-6c}\)

1) Разложим знаменатели: \(9-x^2=-(x-3)(x+3)\), \(2x-6=2(x-3)\).

\[\frac{2x}{9-x^2}-\frac{1}{2x-6}=-\frac{2x}{(x-3)(x+3)}-\frac{1}{2(x-3)}.\]

Приведём к общему знаменателю:

\[\frac{-4x-(x+3)}{2(x-3)(x+3)}=-\frac{5x+3}{2(x-3)(x+3)}.\]

3) \(4c^2-25=(2c-5)(2c+5)\), \(15-6c=-3(2c-5)\).

\[\frac{2}{(2c-5)(2c+5)}-\frac{c}{2c-5}=\frac{2-c(2c+5)}{(2c-5)(2c+5)}.\]

\[\frac{2-2c^2-5c}{(2c-5)(2c+5)}.\]

Ответ: 1) \(-\frac{5x+3}{2(x-3)(x+3)}\); 3) \(\frac{2-2c^2-5c}{(2c-5)(2c+5)}\).