Решения:

1) $$\frac{3}{x+y} + \frac{2}{x} - \frac{5x+2y}{x(x+y)} = \frac{3x + 2(x+y) - (5x+2y)}{x(x+y)} = \frac{3x + 2x + 2y - 5x - 2y}{x(x+y)} = \frac{0}{x(x+y)} = 0$$ 2) $$\frac{a}{a+1} + \frac{1}{a-1} = \frac{a(a-1) + 1(a+1)}{(a+1)(a-1)} = \frac{a^2 - a + a + 1}{a^2 - 1} = \frac{a^2 + 1}{a^2 - 1}$$ 3) $$\frac{4}{x-3} + \frac{1}{x+3} = \frac{4(x+3) + 1(x-3)}{(x-3)(x+3)} = \frac{4x + 12 + x - 3}{x^2 - 9} = \frac{5x + 9}{x^2 - 9}$$ 4) $$\frac{c-1}{c+2} - \frac{c-2}{c+1} = \frac{(c-1)(c+1) - (c-2)(c+2)}{(c+2)(c+1)} = \frac{c^2 - 1 - (c^2 - 4)}{(c+2)(c+1)} = \frac{c^2 - 1 - c^2 + 4}{(c+2)(c+1)} = \frac{3}{(c+2)(c+1)}$$ 5) $$\frac{x+b}{3x} - \frac{x}{x+b} = \frac{(x+b)(x+b) - x(3x)}{3x(x+b)} = \frac{x^2 + 2xb + b^2 - 3x^2}{3x(x+b)} = \frac{-2x^2 + 2xb + b^2}{3x(x+b)}$$ 6) $$\frac{a-b}{a+b} - \frac{a+b}{a-b} = \frac{(a-b)(a-b) - (a+b)(a+b)}{(a+b)(a-b)} = \frac{a^2 - 2ab + b^2 - (a^2 + 2ab + b^2)}{a^2 - b^2} = \frac{a^2 - 2ab + b^2 - a^2 - 2ab - b^2}{a^2 - b^2} = \frac{-4ab}{a^2 - b^2}$$ 7) $$\frac{3ab-a^2}{(a-b)(a+b)} + \frac{2a}{a-b} = \frac{3ab - a^2 + 2a(a+b)}{(a-b)(a+b)} = \frac{3ab - a^2 + 2a^2 + 2ab}{(a-b)(a+b)} = \frac{a^2 + 5ab}{(a-b)(a+b)} = \frac{a(a+5b)}{(a-b)(a+b)}$$ 8) $$\frac{2y}{y-x} - \frac{3x}{y+x} = \frac{2y(y+x) - 3x(y-x)}{(y-x)(y+x)} = \frac{2y^2 + 2xy - 3xy + 3x^2}{y^2 - x^2} = \frac{2y^2 - xy + 3x^2}{y^2 - x^2}$$ 9) $$\frac{1}{a^2} + \frac{1}{a} = \frac{1 + a}{a^2}$$ 9) $$\frac{x}{(a-b)^2} + \frac{2}{5(a-b)} = \frac{5x + 2(a-b)}{5(a-b)^2} = \frac{5x + 2a - 2b}{5(a-b)^2}$$ 10) $$\frac{2y}{x^2 - x} = \frac{2y}{x(x - 1)}$$ 10) $$\frac{b}{(x-y)^2} + \frac{10}{3(x-y)} = \frac{3b + 10(x-y)}{3(x-y)^2} = \frac{3b + 10x - 10y}{3(x-y)^2}$$