Minimum and maximum..?

Algebra Level 4

The inequality:

ax42x2+3(x2+1)2ba\le \frac { { x }^{ 4 }-2{ x }^{ 2 }+3 }{ { ({ x }^{ 2 }+1) }^{ 2 } } \le b

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

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