SOLUTION: prove, if x,y ∈ Q
then there are integers a,b,c
such that x=a/c and y=b/c
Algebra.Com
Question 1042996: prove, if x,y ∈ Q
then there are integers a,b,c
such that x=a/c and y=b/c
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Since x and y are rational there exist
integers d and e such that
and integers f and g such that
Notice that
= =
and
= =
So we have and
Since the product of two integers is an integer,
we can set c = eg where c is an integer
set a = dg where a is an integer
set b = fe where b is an integer
Substituting we have
and
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