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

Ответ:

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

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

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

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