add, express answer in simplest form

Question

4x/x^2-18x+72 + 4/x-6

Answer 1

For this question to make sense, I will assume you meant:

4x/(x^2-18x+72) + 4/(x-6)

the first denominator factors to (x-6)(x-12), so it becomes your lowest common denominator

then
4x/(x^2-18x+72) + 4/(x-6)
= 4x/[(x-6)(x-12)] + 4/(x-6)
=[4x(x-6) + 4] / [(x-6)(x-12)]
= [4x^2 - 24x + 4} / [(x-6)(x-12)]

(really not much of a "simplification" problem), the original looks even simpler.

Answer 2

subtract 4x/x-8-32/x-8

Answer 3

-2x > x-12