Упростите выражение: 3) \(\frac{5a}{a+3}+\frac{a-6}{3a+9}\cdot\frac{135}{6a-a^2}\).

ОДЗ: \(a\ne -3,\ a\ne 0,\ a\ne 6\).

\[\frac{a-6}{3(a+3)}\cdot\frac{135}{a(6-a)}=-\frac{45}{a(a+3)}.\]

\[\frac{5a}{a+3}-\frac{45}{a(a+3)}=\frac{5a^2-45}{a(a+3)}=\frac{5(a-3)(a+3)}{a(a+3)}=\frac{5(a-3)}a.\]

Ответ: \(\frac{5(a-3)}a\).