Answer
$3x^3+5x+4-\dfrac{2x}{x^2-2}$
Work Step by Step
Using the long division method below, then
\begin{array}{l}\require{cancel}(
3x^5-x^3+4x^2-12x-8
)\div(
x^2-2
)\\=
3x^3+5x+4-\dfrac{2x}{x^2-2}
.\end{array}
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