5. $$ \frac{12p^3q^2-3pq^4}{4p^2q^2+2pq^3} $$

Решение:

$$ \frac{12p^3q^2-3pq^4}{4p^2q^2+2pq^3} = \frac{3pq^2(4p^2-q^2)}{2pq^2(2p+q)} = \frac{3(2p-q)(2p+q)}{2(2p+q)} = \frac{3(2p-q)}{2} $$

Ответ: $$ \frac{3(2p-q)}{2} $$