+556 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?
+129830 3/x makes 0 not in the range
2 / (1 + 3/x) = 2 / [ (x + 3) /x ] = [2x ] / (x + 3) makes - 3 not in the range
1 + (2x) / ( x + 3) = [ (x + 3)+ 2x ] / (x +3) = [ 3x + 3 ] / (x + 3)
So
1 / [ (3x + 3) / ( x + 3) ] = (x + 3) / (3x + 3) makes -1 not in the range
Sum of three numbers = 0 + (- 3) + ( -1 ) = -4
