Answer
$x^2 +\frac{x-2}{3x^3-1}$
Work Step by Step
We use the long division as shown in the figure below.
Checking:
$$
(3x^3-1)(x^2 )+x-2=3x^5-x^2 +x-2
$$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/c7e12e47-4767-40c3-a0c5-1234bb9d5558/steps_image/small_1586429012.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T002025Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=3718b77782777d6abb5ef0acb517a08f79169f102c96983f741662663d4b2c50)
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