Представьте в виде дроби: a) $$rac{14p^{4}}{q^{6}} : \frac{56p^{4}}{q^{2}}$$; б) $$rac{45a^{3}b}{c^{2}} : \frac{30a^{4}b}{c^{4}}$$; в) $$\frac{3a-9}{a+2} : \frac{a^{2}-9}{a^{2}-4}$$; г) $$\frac{3x+y}{y} : (\frac{y}{x} - \frac{3y}{3x+y})$$.

Определим предмет: алгебра. а) $$\frac{14p^{4}}{q^{6}} : \frac{56p^{4}}{q^{2}} = \frac{14p^{4}}{q^{6}} \cdot \frac{q^{2}}{56p^{4}} = \frac{14}{56} \cdot \frac{p^{4}}{p^{4}} \cdot \frac{q^{2}}{q^{6}} = \frac{1}{4} \cdot 1 \cdot \frac{1}{q^{4}} = \frac{1}{4q^{4}}$$ <p><strong>Ответ: $$\frac{1}{4q^{4}}$$.</strong></p> б) $$\frac{45a^{3}b}{c^{2}} : \frac{30a^{4}b}{c^{4}} = \frac{45a^{3}b}{c^{2}} \cdot \frac{c^{4}}{30a^{4}b} = \frac{45}{30} \cdot \frac{a^{3}}{a^{4}} \cdot \frac{b}{b} \cdot \frac{c^{4}}{c^{2}} = \frac{3}{2} \cdot \frac{1}{a} \cdot 1 \cdot c^{2} = \frac{3c^{2}}{2a}$$ <p><strong>Ответ: $$\frac{3c^{2}}{2a}$$.</strong></p> в) $$\frac{3a-9}{a+2} : \frac{a^{2}-9}{a^{2}-4} = \frac{3(a-3)}{a+2} : \frac{(a-3)(a+3)}{(a-2)(a+2)} = \frac{3(a-3)}{a+2} \cdot \frac{(a-2)(a+2)}{(a-3)(a+3)} = 3 \cdot \frac{a-2}{a+3}$$ <p><strong>Ответ: $$\frac{3(a-2)}{a+3}$$.</strong></p> г) $$\frac{3x+y}{y} : (\frac{y}{x} - \frac{3y}{3x+y}) = \frac{3x+y}{y} : (\frac{y(3x+y) - 3xy}{x(3x+y)}) = \frac{3x+y}{y} : (\frac{3xy+y^{2} - 3xy}{x(3x+y)}) = \frac{3x+y}{y} : (\frac{y^{2}}{x(3x+y)}) = \frac{3x+y}{y} \cdot \frac{x(3x+y)}{y^{2}} = \frac{x(3x+y)^{2}}{y^{3}}$$ <p><strong>Ответ: $$\frac{x(3x+y)^{2}}{y^{3}}$$.</strong></p>