6) (c-4)/(4c+24) + (4c+9)/(c²+6c).

6) Упростим выражение:

$$\frac{c-4}{4c+24} + \frac{4c+9}{c^2+6c} = \frac{c-4}{4(c+6)} + \frac{4c+9}{c(c+6)} = \frac{c(c-4)}{4c(c+6)} + \frac{4(4c+9)}{4c(c+6)} = \frac{c^2-4c+16c+36}{4c(c+6)} = \frac{c^2+12c+36}{4c(c+6)} = \frac{(c+6)^2}{4c(c+6)} = \frac{c+6}{4c}$$

Ответ: $$\frac{c+6}{4c}$$