[?] Avoid division by zero?

Questions
1

Hello, I have two lists

p={2,5,-6,8,3}

and

q ={3,-4,0,5,0}

I want to get the list

p/q = {2/3,5/-4,8/5}

which is obtained by dividing elements of p by elements of q one by one avoiding division by zeros. Code p/q yields

"infinite expression 1/0 encountered"

Please help.
Thanks and regards

2

p = {2, 5, -6, 8, 3}; q = {3, -4, 0, 5, 0};

Off[Power::infy]

Select[p/q, NumberQ[#] &]

{2/3, -(5/4), 8/5}
3

Divide @@@ Pick[Transpose[{p, q}], Unitize@q, 1]

4

Hello Frank,
Thanks a lot. It helped me write a code for simplex method in OR.

5

Elegant !