Решение

1. $$\frac{x-3}{3x+6} - \frac{x-6}{x+2} = \frac{x-3}{3(x+2)} - \frac{x-6}{x+2} = \frac{x-3 - 3(x-6)}{3(x+2)} = \frac{x-3 - 3x + 18}{3(x+2)} = \frac{-2x + 15}{3(x+2)}$$
2. $$\frac{m+4}{5m-10} + \frac{3-m}{4m-8} = \frac{m+4}{5(m-2)} + \frac{3-m}{4(m-2)} = \frac{4(m+4) + 5(3-m)}{20(m-2)} = \frac{4m+16 + 15 - 5m}{20(m-2)} = \frac{-m + 31}{20(m-2)}$$
3. $$\frac{y+6}{y-6} - \frac{y+2}{y+6} = \frac{(y+6)(y+6) - (y+2)(y-6)}{(y-6)(y+6)} = \frac{y^2 + 12y + 36 - (y^2 - 6y + 2y - 12)}{y^2 - 36} = \frac{y^2 + 12y + 36 - y^2 + 4y + 12}{y^2 - 36} = \frac{16y + 48}{y^2 - 36} = \frac{16(y+3)}{(y-6)(y+6)}$$

Ответ:

1. $$\frac{-2x + 15}{3(x+2)}$$
2. $$\frac{-m + 31}{20(m-2)}$$
3. $$\frac{16(y+3)}{(y-6)(y+6)}$$