2. Представьте выражение в виде дроби: a) \(\frac{28p^4q^5}{9q^6} \div \frac{56p^4}{q^4}\); б) \(\frac{72x^3y}{z} \div (30x^2y)\); в) \(\frac{x^2-1}{x^2-9} \cdot \frac{5x+10}{x-1}\); г) \(\frac{y+c}{c} + (\frac{c}{y} + \frac{c}{y+c})\).

a) \(\frac{28p^4q^5}{9q^6} \div \frac{56p^4}{q^4}\) = \(\frac{28p^4q^5}{9q^6} \cdot \frac{q^4}{56p^4}\). Сокращаем 28 и 56, получаем \(\frac{1}{2}\). Сокращаем \(p^4\) и \(p^4\), получаем 1. Сокращаем \(q^5\) и \(q^6\), получаем \(\frac{1}{q}\). Умножаем на \(q^4\), получаем \(\frac{q^4}{q}=q^3\). Итого, \(\frac{q^3}{18}\).

б) \(\frac{72x^3y}{z} \div (30x^2y)\) = \(\frac{72x^3y}{z} \cdot \frac{1}{30x^2y}\). Сокращаем 72 и 30, получаем \(\frac{12}{5}\). Сокращаем \(x^3\) и \(x^2\), получаем x. Сокращаем y и y, получаем 1. Итого, \(\frac{12x}{5z}\).

в) \(\frac{x^2-1}{x^2-9} \cdot \frac{5x+10}{x-1}\) = \(\frac{(x-1)(x+1)}{(x-3)(x+3)} \cdot \frac{5(x+2)}{x-1}\). Сокращаем (x-1). Получаем \(\frac{(x+1)5(x+2)}{(x-3)(x+3)}\) = \(\frac{5(x+1)(x+2)}{(x-3)(x+3)}\).

г) \(\frac{y+c}{c} + (\frac{c}{y} + \frac{c}{y+c})\) = \(\frac{y+c}{c} + \frac{c(y+c) + cy}{y(y+c)}\) = \(\frac{y+c}{c} + \frac{cy+c^2 + cy}{y(y+c)}\) = \(\frac{y+c}{c} + \frac{2cy+c^2}{y(y+c)}\) = \(\frac{(y+c)y(y+c) + c(2cy+c^2)}{cy(y+c)}\) = \(\frac{y(y+c)^2 + 2c^2y + c^3}{cy(y+c)}\) = \(\frac{y(y^2+2yc+c^2) + 2c^2y + c^3}{cy(y+c)}\) = \(\frac{y^3+2y^2c+yc^2 + 2c^2y + c^3}{cy(y+c)}\) = \(\frac{y^3+2y^2c+3yc^2 + c^3}{cy(y+c)}\).

Ответ: а) \(\frac{q^3}{18}\); б) \(\frac{12x}{5z}\); в) \(\frac{5(x+1)(x+2)}{(x-3)(x+3)}\); г) \(\frac{y^3+2y^2c+3yc^2 + c^3}{cy(y+c)}\)