Решение выражений:

1. 2) $$\frac{4x}{x^2-y^2} - \frac{4}{x+y} = \frac{4x}{(x-y)(x+y)} - \frac{4}{x+y} = \frac{4x - 4(x-y)}{(x-y)(x+y)} = \frac{4x - 4x + 4y}{(x-y)(x+y)} = \frac{4y}{(x-y)(x+y)}$$

2. 4) $$\frac{15a^2}{3a-2} - 5a = \frac{15a^2 - 5a(3a-2)}{3a-2} = \frac{15a^2 - 15a^2 + 10a}{3a-2} = \frac{10a}{3a-2}$$

3. 6) $$\frac{20}{c^2+4c} - \frac{5}{c^2} = \frac{20}{c(c+4)} - \frac{5}{c^2} = \frac{20c - 5(c+4)}{c^2(c+4)} = \frac{20c - 5c - 20}{c^2(c+4)} = \frac{15c - 20}{c^2(c+4)} = \frac{5(3c-4)}{c^2(c+4)}$$

4. 8) $$\frac{a^2}{a^2-1} - \frac{a}{a+1} = \frac{a^2}{(a-1)(a+1)} - \frac{a}{a+1} = \frac{a^2 - a(a-1)}{(a-1)(a+1)} = \frac{a^2 - a^2 + a}{(a-1)(a+1)} = \frac{a}{(a-1)(a+1)}$$

5. 10) $$\frac{a^2+y^2}{ay-y^2} - \frac{2a}{a-y} = \frac{a^2+y^2}{y(a-y)} - \frac{2a}{a-y} = \frac{a^2+y^2 - 2ay}{y(a-y)} = \frac{(a-y)^2}{y(a-y)} = \frac{a-y}{y}$$

6. 12) $$\frac{3b^2+2b}{b^2-4} - \frac{b}{b-2} = \frac{3b^2+2b}{(b-2)(b+2)} - \frac{b}{b-2} = \frac{3b^2+2b - b(b+2)}{(b-2)(b+2)} = \frac{3b^2+2b - b^2 - 2b}{(b-2)(b+2)} = \frac{2b^2}{(b-2)(b+2)}$$