When dividing rational expressions (P(x)/Q(x) divided by R(x)/S(x)), is this expression undefined when any of Q(x), R(x), or S(x) undefined?

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When dividing rational expressions (P(x)/Q(x) divided by R(x)/S(x)), is this expression undefined when any of Q(x), R(x), or S(x) undefined?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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my guess is yes; when a peice is undefined that usually puts a damper on things
Sorry, I meant when any of those 3 are 0.
Q(x) cant be zero; and R(x) cant be zerp

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Other answers:

zerp is like a zero but only got its GED
S(x) can't be zero either though, because if it were, S(x)/R(x) would be 0 and that would be dividing the first part by 0, right?
You are correct
Sorry, I got screwed up, I meant it would make S(x)/R(x) undefined and thus the whole thing. Okay, I just wanted to make sure it was any of the 3.
P(x) ---- Q(x) <- cant be zero ------- R(x) <- cant be zero --- S(x) <- cant be zero
Perfect.

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