After x+1 over 3 minus x+2 over 2x have been combined using the least common denominator of 6x what is the numerator

the common denominator is 6x

we multiply the first term by 2x/2x and the second term by 3/3

(x+1) / 3 * 2x/2x - (x+2) / 2x * (3/3)

2x (x+1) / 6x - (x+2) * 3/6x

distribute

(2x^2+2x - 3x-6) / 6x

(2x^2-x-6) / 6x

The numerator is (2x^2-x-6)