Let
$$f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.$$
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?
1 answer
The fraction in $f(x)$ becomes undefined if and only if the denominator $1+\frac 3x$ becomes 0. We have $1+\frac 3x = 0$ if and only if $\frac 3x = -1$ if and only if $x = \boxed{-3}$. (If $1 + \frac 3x = 0$, then $1 = -\frac 3x$, then $x = -\frac 3 1 = -3$.)