5) Выполните деление:

\(\frac{x+1}{3x} : \frac{x^2+2x+1}{9x^2} = \frac{x+1}{3x} \cdot \frac{9x^2}{x^2+2x+1} = \frac{x+1}{3x} \cdot \frac{9x^2}{(x+1)^2} = \frac{3x}{x+1}\)

\(\frac{x^2-2x}{3x+3} : \frac{5x-10}{x+1} = \frac{x(x-2)}{3(x+1)} \cdot \frac{x+1}{5(x-2)} = \frac{x}{15}\)

\((n-7) : \frac{n^2-14n+49}{n^2-49} = (n-7) \cdot \frac{n^2-49}{n^2-14n+49} = (n-7) \cdot \frac{(n-7)(n+7)}{(n-7)^2} = n+7\)

\(\frac{a^2-4b^2}{9a^2-b^2} : \frac{a^2+4ab+4b^2}{9a^2-6ab+b^2} = \frac{(a-2b)(a+2b)}{(3a-b)(3a+b)} \cdot \frac{(3a-b)^2}{(a+2b)^2} = \frac{(a-2b)(3a-b)}{(3a+b)(a+2b)}\)