Question

Dear fellow thinkers,

Might I ask for your help in looking for a proof in the subject of Calculus?

Let f and g be two real functions, both continuous in a ∈ ℝ. Who has a proof for the following:
If g(a)≠0, then f/g is continuous in a.

P.S.: My calculus course uses (ε, δ)-definitions of intervals for similar proofs.

Dear regards,

Vincent