Two functions f/g Uniform Continuity

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I was wondering if f and g are two uniformly continuous functions on a set such that g(x) is not zero is f/g uniformly continuous?


I have a feeling it is not but I can't seem to find a counter example.
 
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The function 1/x on ]0,1] should probably be a good counterexample...
 
But 1 is not considering a function f is it?
 
Take f(x)=1, the constant function, and g(x)=x...
 
If D is compact then f/g will be uniformly continuous on D right?
 
Yes. That's why I took the interval ]0,1].
 

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