Answer
$2x^2+\frac{-x^2+x+1}{2x^3-1}$
Work Step by Step
We use the long division as be shown in the figure below.
Checking:
$$
(2x^3-1)(2x^2)-x^2+x+1\\
=4x^5-2x^2-x^2+x+1\\
=4x^5-3x^2+x+1
$$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9afa150e-25c5-4371-8cda-6aa6e998224e/steps_image/small_1586347448.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000044Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=a730876e62e622406e8fa50109f64e8c11c9d64fe435bac656010c87a37e4b4a)
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