Упростите выражение: (a+9)/(3a+9)-(a+3)/(3a-9)+13/(a^2-9).

Ответ:

\[\frac{a + 9}{3a + 9} - \frac{a + 3}{3a - 9} + \frac{13}{a^{2} - 9} =\]

\[= \frac{a + 9}{3(a + 3)} - \frac{a + 3}{3(a - 3)} + \frac{13}{(a - 3)(a + 3)} =\]

\[= \frac{(a + 9)(a - 3) - (a + 3)(a + 3) + 13 \cdot 3}{3(a - 3)(a + 3)} =\]

\[= \frac{a^{2} + 9a - 3a - 27 - a^{2} - 6a - 9 + 39}{3\left( a^{2} - 9 \right)} =\]

\[= \frac{3}{3(a^{2} - 9)} = \frac{1}{a^{2} - 9}.\]