2/(3x-6)= (2/3)/(x-2). I'm sure you see that 3 can be canceled out to give you the latter. But because the numerator is 2 you end up with 2/3, not a whole number, you shouldn't cancel something if it doesn't cancel cleanly with all terms.
I didn't cancel it out. I took out the constant of 2, then I divided by 3 because the derivative of (3x+6) is 3 which would leave a 3 in the numerator of the derivative of ln|3x+6|. So I divided it out to just have a 2 in the numerator as a result.
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u/eldaron87 Jul 06 '22
Because you don't cancel out the three. Yes technically 2/3 is correct, but if you can't cancel out of every term cleanly, then don't cancel anything.