uniform continuity of quotient of two uniform continuous functions

Question

as we know quotient $\frac{f(x)}{g(x)}$ of two real valued continuous functions $f(x)$ and $g(x)$ defined on $\mathbb R$ and so that $g(x) \neq 0\ \forall x \in \mathbb R $ is continuous. What can we say about the quotient of two uniformly continuous functions?

Answer 1

It seems that the function $f(x)=\exp(-|x|)$ is uniformly continuous on $\mathbb R$, but $1/f(x)=\exp(|x|)$ is not.

Answer 2

No: $$\dfrac{\dfrac{t^2}{1+t^4}}{\dfrac{1}{1+t^4}}.$$