Let $x,$ $y,$ and $z$ be real numbers such that $x + y + z = 6$ and $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 2.$  Find
\[\frac{x + y}{z} + \frac{y + z}{x} + \frac{x + z}{y}.\]
Question:
Let $x,$ $y,$ and $z$ be real numbers such that $x + y + z = 6$ and $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 2.$  Find
\[\frac{x + y}{z} + \frac{y + z}{x} + \frac{x + z}{y}.\]
Answer:
Let's think step by step.

user
9
Let $x,$ $y,$ and $z$ be real numbers such that $x + y + z = 6$ and $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 2.$  Find
\[\frac{x + y}{z} + \frac{y + z}{x} + \frac{x + z}{y}.\]
train