SOLUTION: If x, y ∈ Q then there are integers a, b, c such that x = a/c and y =b/c Can this be proven using a proof or is there a solid counterexample? .

SOLUTION: If x, y ∈ Q then there are integers a, b, c such that x = a/c and y =b/c Can this be proven using a proof or is there a solid counterexample? .

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Question 1042956: If x, y ∈ Q then there are integers a, b, c such that x = a/c and y =b/c
Can this be proven using a proof or is there a solid counterexample?
.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Statement is true.

x and y are rational by definition, so let c equal the least common denominator of x and y. Then you can find a and b such that x = a/c and y = b/c.

Formally, let

and

where p, q, r, s are integers,

and

,

(i.e. fractions in simplest form). Then

,

and

is an example set of values.
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