5. Сократить дробь: a) y²+yx / y³ б) 2a-3a / 4a²-9a² в) a³+5a / a²-25 г) ac-2bc+2b-a / a²-4ab+4b²

a) $$ \frac{y^2 + yx}{y^3} = \frac{y(y + x)}{y^3} = \frac{y + x}{y^2} $$

б) $$ \frac{2a-3a}{4a^2 - 9a^2} = \frac{-a}{-5a^2} = \frac{1}{5a} $$

в) $$ \frac{a^3 + 5a}{a^2 - 25} = \frac{a(a^2 + 5)}{(a - 5)(a + 5)} $$

г) $$ \frac{ac - 2bc + 2b - a}{a^2 - 4ab + 4b^2} = \frac{c(a - 2b) - (a - 2b)}{(a - 2b)^2} = \frac{(c - 1)(a - 2b)}{(a - 2b)^2} = \frac{c - 1}{a - 2b} $$