8. $$ \frac{125-8v^3}{25v^2-4} $$

Решение:

$$ \frac{125-8v^3}{25v^2-4} = \frac{(5-2v)(25+10v+4v^2)}{(5v-2)(5v+2)} = \frac{-(2v-5)(25+10v+4v^2)}{(5v-2)(5v+2)} = \frac{-(25+10v+4v^2)}{5v+2} $$

Ответ: $$ -\frac{25+10v+4v^2}{5v+2} $$