\[\frac{{x}^{3}-4x+1}{{x}^{2}-4}\]
1
Polynomial Division: Divide x3−4x+1{x}^{3}-4x+1 by x2−4{x}^{2}-4.

xx
x2−4x^2-4x3x^3−4x-4x11
x3x^3−4x-4x
11

2
Rewrite the expression using the above.
x+1x2−4x+\frac{1}{{x}^{2}-4}

Done
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