# Minimum and maximum..?

Algebra Level 4

The inequality:

$a\le \frac { { x }^{ 4 }-2{ x }^{ 2 }+3 }{ { ({ x }^{ 2 }+1) }^{ 2 } } \le b$

is always true for any real number $$x.$$ If $$m$$ represents the maximum possible value of $$a,$$ and $$n$$ represents the minimum possible value of $$b,$$ what is the value of $$mn?$$

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