Решение:

1. a) $$\frac{3}{5x^2y} - \frac{2}{3xy^2} = \frac{3 \cdot 3y}{5x^2y \cdot 3y} - \frac{2 \cdot 5x}{3xy^2 \cdot 5x} = \frac{9y}{15x^2y^2} - \frac{10x}{15x^2y^2} = \frac{9y - 10x}{15x^2y^2}$$
2. б) $$\frac{4}{y^2 - 4} - \frac{1}{y - 2} = \frac{4}{(y - 2)(y + 2)} - \frac{1}{y - 2} = \frac{4}{(y - 2)(y + 2)} - \frac{1 \cdot (y + 2)}{(y - 2) \cdot (y + 2)} = \frac{4 - (y + 2)}{(y - 2)(y + 2)} = \frac{4 - y - 2}{(y - 2)(y + 2)} = \frac{2 - y}{(y - 2)(y + 2)} = -\frac{y - 2}{(y - 2)(y + 2)} = -\frac{1}{y + 2}$$
3. в) $$\frac{2}{a + b} + \frac{3a + 3b}{a^2 + 2ab + b^2} = \frac{2}{a + b} + \frac{3(a + b)}{(a + b)^2} = \frac{2}{a + b} + \frac{3}{a + b} = \frac{2 + 3}{a + b} = \frac{5}{a + b}$$
4. г) $$\frac{6}{5a - 10} - \frac{2}{3a - 6} = \frac{6}{5(a - 2)} - \frac{2}{3(a - 2)} = \frac{6 \cdot 3}{5(a - 2) \cdot 3} - \frac{2 \cdot 5}{3(a - 2) \cdot 5} = \frac{18}{15(a - 2)} - \frac{10}{15(a - 2)} = \frac{18 - 10}{15(a - 2)} = \frac{8}{15(a - 2)}$$
5. д) $$\frac{1}{x^2 - xy} - \frac{1}{xy - y^2} = \frac{1}{x(x - y)} - \frac{1}{y(x - y)} = \frac{1 \cdot y}{x(x - y) \cdot y} - \frac{1 \cdot x}{y(x - y) \cdot x} = \frac{y}{xy(x - y)} - \frac{x}{xy(x - y)} = \frac{y - x}{xy(x - y)} = -\frac{x - y}{xy(x - y)} = -\frac{1}{xy}$$