Решение:

1. а) $$rac{a}{6} + \frac{b}{6} = \frac{a+b}{6}$$
   Ответ: $$rac{a+b}{6}$$
2. б) $$rac{p}{3} - \frac{q}{3} = \frac{p-q}{3}$$
   Ответ: $$rac{p-q}{3}$$
3. в) $$rac{x}{y} + \frac{3x}{y} = \frac{x+3x}{y} = \frac{4x}{y}$$
   Ответ: $$rac{4x}{y}$$
4. г) $$rac{5m}{n} - \frac{3m}{n} = \frac{5m-3m}{n} = \frac{2m}{n}$$
   Ответ: $$rac{2m}{n}$$
5. д) $$rac{x+4y}{12} + \frac{2x+5y}{12} = \frac{x+4y+2x+5y}{12} = \frac{3x+9y}{12} = \frac{3(x+3y)}{12} = \frac{x+3y}{4}$$
   Ответ: $$\frac{x+3y}{4}$$
6. е) $$\frac{a+2b}{2c} - \frac{a-4b}{2c} = \frac{a+2b-(a-4b)}{2c} = \frac{a+2b-a+4b}{2c} = \frac{6b}{2c} = \frac{3b}{c}$$
   Ответ: $$\frac{3b}{c}$$
7. ж) $$\frac{-4c+3d}{cd} + \frac{3d-c}{cd} = \frac{-4c+3d+3d-c}{cd} = \frac{-5c+6d}{cd} = \frac{6d-5c}{cd}$$
   Ответ: $$\frac{6d-5c}{cd}$$