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

user
2
Let $x,$ $y,$ $z$ be real numbers such that $-1 < x,$ $y,$ $z < 1.$  Find the minimum value of
\[\frac{1}{(1 - x)(1 - y)(1 - z)} + \frac{1}{(1 + x)(1 + y)(1 + z)}.\]
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