Решение:

1. a) $$\frac{9x^6}{y^3} : \frac{6x^4}{y^5} = \frac{9x^6}{y^3} \cdot \frac{y^5}{6x^4} = \frac{9x^6y^5}{6x^4y^3} = \frac{3x^2y^2}{2}$$.

2. б) $$\frac{4x^3}{x+2} \cdot \frac{x^2+4x+4}{8x^2} = \frac{4x^3}{x+2} \cdot \frac{(x+2)^2}{8x^2} = \frac{4x^3(x+2)^2}{8x^2(x+2)} = \frac{x(x+2)}{2}$$.

3. в) $$\frac{3a-9}{a+2} : \frac{a^2-9}{a^2-4} = \frac{3(a-3)}{a+2} : \frac{(a-3)(a+3)}{(a-2)(a+2)} = \frac{3(a-3)}{a+2} \cdot \frac{(a-2)(a+2)}{(a-3)(a+3)} = \frac{3(a-2)}{a+3}$$.

Ответ:

1. $$\frac{3x^2y^2}{2}$$
2. $$\frac{x(x+2)}{2}$$
3. $$\frac{3(a-2)}{a+3}$$