There are three real numbers $x$ that are not in the domain of
$$f(x) = \frac{1}{1+\frac{1}{1+\frac 1x}}.$$
What is the sum of those three numbers?
Well we cannot divide by 0 so
\(x\ne0\)
\(1+\frac{1}{x}\ne0\\ \frac{1}{x}\ne-1\\ x\ne-1 \)
\(1+\frac{1}{1+\frac{1}{x}}\ne0\\ \frac{1}{1+\frac{1}{x}}\ne-1\\ \frac{x}{x+1}\ne-1\\ x\ne -x-1\\ 2x\ne-1\\ x\ne -\frac{1}{2}\)
+193 
