How do you find the domain for #f(x)=(1+3x)/(5-2x)#?
The domain means anywhere where there's actually a graph. So for there to be no graph, you can't have a number which in this and pretty much all of these cases are where y goes to infinity as x progresses.
Any number divided by 0 is going to be undefined, where y goes to infinity.
So your goal is to make the denominator in that fraction a 0 so that you'll divide by it and find somewhere where the graph doesn't exist.
The algebra, then, is pretty simple.
So then put that into the parentheses domain where the graph goes from x=infinity to 2/5 to y=infinity