Сократите дробь: а) \(\frac{21a^3b^5}{35a^4b^2}\); б) \(\frac{6x^3\cdot(x+y)}{9xy\cdot(x+y)}\); в) \(\frac{5m-5n}{m^2n-mn^2}\); г) \(\frac{4a^2-9}{10a+15}\); д) \(\frac{a^2+2ab+b^2}{a^2-b^2}\); е) \(\frac{x^3+1}{x^2+x}\).

1. \(\frac{21a^3b^5}{35a^4b^2}=\frac{3b^3}{5a}\).
2. \(\frac{6x^3(x+y)}{9xy(x+y)}=\frac{2x^2}{3y}\).
3. \(\frac{5m-5n}{m^2n-mn^2}=\frac{5(m-n)}{mn(m-n)}=\frac{5}{mn}\).
4. \(\frac{4a^2-9}{10a+15}=\frac{(2a-3)(2a+3)}{5(2a+3)}=\frac{2a-3}{5}\).
5. \(\frac{a^2+2ab+b^2}{a^2-b^2}=\frac{(a+b)^2}{(a-b)(a+b)}=\frac{a+b}{a-b}\).
6. \(\frac{x^3+1}{x^2+x}=\frac{(x+1)(x^2-x+1)}{x(x+1)}=\frac{x^2-x+1}{x}\).

Ответ: а) \(\frac{3b^3}{5a}\); б) \(\frac{2x^2}{3y}\); в) \(\frac{5}{mn}\); г) \(\frac{2a-3}{5}\); д) \(\frac{a+b}{a-b}\); е) \(\frac{x^2-x+1}{x}\).