Упростите выражение (a+12)/(4a+16)-(a+4)/(4a-16)+19/(a^2-16).

\[\frac{a + 12}{4a + 16} - \frac{a + 4}{4a - 16} + \frac{19}{a^{2} - 16} =\]

\[= \frac{a + 12^{\backslash a - 4}}{4(a + 4)} - \frac{a + 4^{\backslash a + 4}}{4(a - 4)} + \frac{19^{\backslash 4}}{(a - 4)(a + 4)} =\]

\[= \frac{a^{2} + 12a - 4a - 48 - a^{2} - 8a - 16 + 76}{4(a - 4)(a + 4)} =\]

\[= \frac{12}{4(a^{2} - 16)} = \frac{3}{a^{2} - 16}\]