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Find $x \in \mathbb R$ so that $\dfrac { x^{ 4 }+3{ x }^{ 2 }+1 }{ { x }^{ 2 } } +\dfrac { { x }^{ 4 }-4{ x }^{ 2 }+1 }{ { x }^{ 3 }+x } = 4$.

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