How do you find the domain for f(x)=(1+3x)/(5-2x)?

$\left(- \infty , \frac{2}{5}\right) \bigcup \left(\frac{2}{5} , \infty\right)$

Explanation:

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.
$5 - 2 x = 0 \to 2 x = 5 \to x = \frac{2}{5}$

So then put that into the parentheses domain where the graph goes from x=infinity to 2/5 to y=infinity
$\left(- \infty , \frac{2}{5}\right) \bigcup \left(\frac{2}{5} , \infty\right)$