Let $x,$ $y,$ $z$ be positive real numbers such that $x + y + z = 1.$  Find the minimum value of
\[\frac{1}{x + y} + \frac{1}{x + z} + \frac{1}{y + z}.\]
Question:
Let $x,$ $y,$ $z$ be positive real numbers such that $x + y + z = 1.$  Find the minimum value of
\[\frac{1}{x + y} + \frac{1}{x + z} + \frac{1}{y + z}.\]
Answer:
Let's think step by step.

user
\frac{9}{2}
Let $x,$ $y,$ $z$ be positive real numbers such that $x + y + z = 1.$  Find the minimum value of
\[\frac{1}{x + y} + \frac{1}{x + z} + \frac{1}{y + z}.\]
train