First, we break up the numerator into its individual terms and write each term over the denominator. We need to deal with the numerator on its own terms. It doesn't like being trifled with.

Then we simplify each new term to find

2x^{3} + 4x^{2} + 3x.

Example 2

Write as a sum of integers.

Pull out a common factor of 2 from the numerator and the denominator, giving us