Question

why is there a vertical asymptote at x=1 for
x/(sin(pi x))

Answer 1

did you try pluggin in 1?

Answer 2

you should get something/zero
where that something isn't zero

Answer 3

so a number over zero is a vertical asymptote?

Answer 4

if the top number isn't 0

Answer 5

oh ok

Answer 6

0/0 could mean you have a hole
but 1/0 definitely means you will have a vertical asymptote

Answer 7

something/0
where the top something isn't 0
means you have a va

0/0 means you could have a hole (it is possible but not a sure thing)