Is LIM (x - > 4) (x ^ 2-4x) / (x ^ 2-3x-4) suitable to use the lobita theorem? What is applicable and what is not. Can't it be used except those two types?

Is LIM (x - > 4) (x ^ 2-4x) / (x ^ 2-3x-4) suitable to use the lobita theorem? What is applicable and what is not. Can't it be used except those two types?

It can be used, because it belongs to the limit of "0 / 0" type, but I don't think it is necessary to use the lobita theorem for this problem, because we can use the decomposition factor to do LIM (x - > 4) (x ^ 2-4x) / (x ^ 2-3x-4) = LIM (x - > 4) x (x-4) / (x + 1) (x-4) = LIM (x - > 4) x / (x + 1) = 4 / (4 + 1) = 4 / 5. Lobita theorem is applicable to "0 / 0" or "