Answer
$$2x^2-x-2+\frac{2}{2x+1}$$
Work Step by Step
Using long division, we find:
$$\frac{(4x^3-5x)}{(2x+1)}\\ 2x^2+\frac{-2x^2-5x}{2x+1}\\ 2x^2-x+\frac{-4x}{2x+1} \\ 2x^2-x-2+\frac{2}{2x+1}$$
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