#### Answer

the domain is: $\{x|x\neq 0,\ -1,\ -2\}$

#### Work Step by Step

We are given:
$f(x)= \frac{1}{x}+\frac{1}{x+1}+\frac{1}{x+2}$
We know that the denominators can't equal 0, so:
$x\ne 0$
$x+1\ne 0$
$x\ne -1$
$x+2\ne 0$
$x\ne -2$
Thus the domain is: $\{x|x\neq 0,\ -1,\ -2\}$.