Question: How to cancel uncommon factors in a set(list)

Hi!

What could be a fast procedure to cancel uncommon factors of terms in such following sets (list) and simplify:

Starting with:

{a*x,b*x, c*(x+y)}

(where a, b and c are numbers or in set of specified variables as well as x and y), I would like as a result:

{x,x+y}

 

Many thanks.

 

Jaqr

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