It really helps to know that the graph of y=(2x) / (x-3) has a vertical asymptote as x=3. The behavior approaching a vertical asymptote is up to infinity or down to negative infinity, those are your choices. If you plug in 3.01 (for x ->3+), then you see it's positive, thus positive infinity. If you plug in 2.99 (for x -> 3-), then you see it's negative, thus negative infinity.