Question 119
Real numbers $x, y, z$ satisfy
$$
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} + x + y + z = 0
$$
and none of them lies in the open interval $(-1, 1)$. Find the maximum value of $x+y+z$.
$$
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} + x + y + z = 0
$$
and none of them lies in the open interval $(-1, 1)$. Find the maximum value of $x+y+z$.