6. $$\frac{c}{c+1} - \frac{c}{c-1} = \frac{c(c-1)}{(c+1)(c-1)} - \frac{c(c+1)}{(c-1)(c+1)} = \frac{c^2 - c - (c^2 + c)}{(c+1)(c-1)} = \frac{c^2 - c - c^2 - c}{(c+1)(c-1)} = \frac{-2c}{c^2 - 1}$$
Ответ: $$\frac{-2c}{c^2 - 1}$$