You may want to review multiplying rational functions first.

To divide two rational functions, you flip the second, then multiply. For example, to divide (x3 + 2x) / (x − 1) by 2, we flip 2, getting 1 / 2, and them multiply, getting (x3 + 2x) / (2x − 2). We would now reduce, but there's nothing to cancel, so we're done.