Simplify (x+3/x^2 -36/x+3) / (x+3/x)
the way you typed it, there is very little simplification
I multiplied top and bottom by x^2 to get
(x^3 + 3 - 36x + 3x^2)/(x^3 + 3x^2) , and that's about it.
If you meant:
( (x+3/x^2 -36/(x+3)) /( (x+3)/x )
it would be something totally different.
I can't guess what you meant.