1. Представьте в виде дроби: a) $$\frac{42x^5}{y^4} \cdot \frac{y^2}{14x^5}$$; б) $$\frac{63a^3b}{c} : (18a^2b)$$; в) $$\frac{4a^2-1}{a^2-9} \cdot \frac{6a+3}{a+3}$$; г) $$\frac{p-q}{p} \cdot (\frac{p}{p-q} + \frac{p}{q})$$

$$\qquad$$а) $$\frac{42x^5}{y^4} \cdot \frac{y^2}{14x^5} = \frac{42 \cdot x^5 \cdot y^2}{14 \cdot x^5 \cdot y^4} = \frac{3}{y^2}$$ $$\qquad$$б) $$\frac{63a^3b}{c} : (18a^2b) = \frac{63a^3b}{c} \cdot \frac{1}{18a^2b} = \frac{63a^3b}{18a^2bc} = \frac{7a}{2c}$$ $$\qquad$$в) $$\frac{4a^2-1}{a^2-9} \cdot \frac{6a+3}{a+3} = \frac{(2a-1)(2a+1)}{(a-3)(a+3)} \cdot \frac{3(2a+1)}{a+3} = \frac{3(2a-1)(2a+1)^2}{(a-3)(a+3)^2}$$ $$\qquad$$г) $$\frac{p-q}{p} \cdot (\frac{p}{p-q} + \frac{p}{q}) = \frac{p-q}{p} \cdot (\frac{pq + p(p-q)}{q(p-q)}) = \frac{p-q}{p} \cdot (\frac{pq + p^2 - pq}{q(p-q)}) = \frac{p-q}{p} \cdot \frac{p^2}{q(p-q)} = \frac{p}{q}$$ $$\qquad$$\textbf{Ответ: } a) $$\frac{3}{y^2}$$; б) $$\frac{7a}{2c}$$; в) $$\frac{3(2a-1)(2a+1)^2}{(a-3)(a+3)^2}$$; г) $$\frac{p}{q}$$