Answer
See below
Work Step by Step
Using synthetic division:
$2x^2+\frac{6x^3-4x^2+4x-17}{3x^2-3x+2}\\=2x^2+2x+\frac{9x^2-17}{3x^2-3x+2}\\=2x^2+2x+3+\frac{10}{3x^2-3x+2}$
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