Actually, you don't have to take them from the non-simplified version. The multiple steps were likely shown for people who want to see every step. If you are confident in using n=8 as the undefined point from just looking at the final result, that's great. In the multiple choice world of Khan Academy problems, all that's needed for a correct answer is the "bottom line". But teachers usually want to see all of the steps that a student took to get that final answer, so it is helpful to see all of the steps in a problem like this one.

Sometimes, too, there are multiple undefined points that are not obvious from the final answer. Suppose the denominator was x^2 - 15x + 56, which is factored as (x - 8) (x - 7). If you set the denominator to zero and solve for n, we get n = 8 or n = 7. Therefore, the values that make the expression undefined are n = 8 and n = 7. If you divide both the numerator and the denominator by n - 8, you get 7 - n instead of 8 - n in the simplified version. This could make you think that the only value of n for which this is undefined is n = 7, not realizing that it is also undefined at n = 8. So it pays to go through all of the steps sometimes.