If i have two closed and disjoint sets A and B in a set X c $R^{m}$, are there any open and disjoint sets in X that contain A and B?

Question

I have a set $X$ $c$ $R^{m}$ and a pair of two closed and disjoint sets in X, called A and B. What i am trying to found at least a pair of sets Y and Z that are open and disjoint in a set X c $R^{m}$ that include A and B, respectively.

For A, i tried using a cover made of all the balls with center in a point of A and an arbitrary ratio intersected with X - A, but if i do the same for B, how could i know if those two covers are disjoint?

Answer 1

See Did's comment. There was an error in my previous solution so I deleted it.