(x+6)/(x-6)<=1

obviously the answer is x<6, but how would i solve this

shit man, engineering student here and I have no idea. Working on it though haha

You can multiply both sides by the denominator squared... in this case (x-6)^2

You then have (x+6)(x-6) ≤ (x-6)^2
x^2 -36 ≤ x^2 - 12x + 36
12x ≤ 72
x ≤ 6

Given that the graph is asymptotic at x = 6 and thus doesn't exist, I guess you drop the 'equal to' portion. I don't really know the proper way to describe that, it's been too long!

Yeah it took me awhile to realize you have to multiply by the denominator squared... whats the reason for this?

holy shit thanks, i knew there was a simple answer i was missing

When you evaluate a limit, you can rationalize the denominator by multiplying by its conjugate

'chr0me357' gave you the answer
but another way is to look at the graph, just visualise it:

starting just below y=1 at the left (minus infinity), then constantly decreasing slowly
crossing y=0 at x=-6, y=-1 at x=0 and then decreasing asymptotically until just before x=6 where is becomes singular
at x=6 it jump from minus infinity to plus infinity and starts decreasing towards y=1