lim x -> 16

(4-√x)/(x-16)

I know you have to do the conjugate (multiply both top and bottom by 4+√x) but then I get (16-x)/(x-16)(4+√x) and i'm not exactly sure how to get the x-16 terms to cancel out, although I know the answer will be negative 1/8. Sorry, i'm not too savvy with algebra.

Furthermore I have a question about limits that don't exist. At what point do you know they don't exist. For example

(2-x)/(x-1)² or (x-1)/x²(x+2) both of which have limits that are undefined/DNE. At what point when attempting to solve them do you realize they don't exist, as opposed to thinking maybe you just haven't done an algebraic trick yet. I know this is pretty ambiguous but if you have any personal tips i'd appreciate it.And finally, thank you alll sooooooooooooooooo much!!! you're so helpful with all of this and i'm envious of you guys lol. Take care!!!