What's going on at 𝑥=𝑐
Let 𝑓𝑥=𝑛𝑥𝑑𝑥
If 𝑛𝑐≠0 and 𝑑𝑐=0,
𝑥=𝑐 is a vertical asymptote
If 𝑛𝑐=0 and 𝑑𝑐=0,
Simplify to find out
There is a hole at −3,−2 
𝑥=−3 is a vertical asymptote.
If 𝑛𝑐=0 and 𝑑𝑐≠0,
𝑥=𝑐 is a zero of 𝑓𝑥.
Graphically, this means 𝑐,0 is an 𝑥-intercept.
𝑥=5 is a zero
5,0 is an 𝑥-intercept
𝑥=−7 is a vertical asymptote