Упростите выражение: (a+3-12a/(a+3))(2a/(a-3)-4a^2/(a^2-6a+9)).

Ответ:

\[\left( a + 3 - \frac{12a}{a + 3} \right)\left( \frac{2a}{a - 3} - \frac{4a^{2}}{a^{2} - 6a + 9} \right) =\]

\[= - 2a\]

\[1)\ (a + 3)^{\backslash a + 3} - \frac{12a}{a + 3} =\]

\[= \frac{a^{2} + 6a + 9 - 12a}{a + 3} = \frac{a^{2} - 6a + 9}{a + 3} =\]

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

\[2)\ \frac{2a}{a - 3} - \frac{4a^{2}}{a^{2} - 6a + 9} = \frac{2a^{\backslash a - 3}}{a - 3} -\]

\[- \frac{4a^{2}}{(a - 3)^{2}} = \frac{2a^{2} - 6a - 4a^{2}}{(a - 3)^{2}} =\]

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

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