After x + 1 / 3 - x + 2 / 2x have been combined using the least common denominator of 6x, what is the numerator?

Answer: The numerator will be 2x^2 - x - 6.

For the first fraction, we need to multiply it by 2x. So we will have:

2x (x + 1) = 2x^2 + 2x

For the second fraction, we need to multiply it by 3. So we will have:

3 (x + 2) = 3x + 6

Now, we just have to subtract the numerators.

2x^2 + 2x - 3x - 6

2x^2 - x - 6