Упростите выражение 3a/(a-3)+(a+5)/(6-2a)*54/(5a+a^2).

Ответ:

\[\frac{3a}{a - 3} + \frac{a + 5}{6 - 2a} \cdot \frac{54}{5a + a^{2}} =\]

\[= \frac{3a}{a - 3} - \frac{(a + 5) \cdot 54}{2 \cdot (a - 3) \cdot a(a + 5)} =\]

\[= \frac{3a^{\backslash a}}{a - 3} - \frac{27}{a(a - 3)} = \frac{3a^{2} - 27}{a(a - 3)} =\]

\[= \frac{3 \cdot \left( a^{2} - 9 \right)}{a(a - 3)} = \frac{3 \cdot (a - 3)(a + 3)}{a(a - 3)} =\]

\[= \frac{3 \cdot (a + 3)}{a} = \frac{3a + 9}{a}\]