Упростите выражение (6/(a^2-9)+1/(3-a))*(a^2+6a+9)/5 и найдите его значение при a=-4.

\[\left( \frac{6}{a^{2} - 9} + \frac{1}{3 - a} \right) \cdot \frac{a^{2} + 6a + 9}{5} =\]

\[1)\ \frac{6}{a^{2} - 9} + \frac{1}{3 - a} =\]

\[= \frac{6}{(a - 3)(a + 3)} - \frac{1^{\backslash a + 3}}{a - 3} =\]

\[= \frac{6 - a - 3}{(a - 3)(a + 3)} =\]

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

\[= \frac{- (a - 3)}{(a - 3)(a + 3)} = - \frac{1}{a + 3}\]

\[2) - \frac{1}{a + 3} \cdot \frac{a^{2} + 6a + 9}{5} =\]

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

\[a = - 4:\]

\[- \frac{- 4 + 3}{5} = - \frac{- 1}{5} = 0,2.\]