Hello all,

While practicing proofs I came across one that I'm having trouble with. Here it is:

Let x and y be non-zero rational numbers. Prove that (4x + 7y) / 6y is a rational number.

Let:

x = a/b . . . where b cannot equal 0

y = c/d . . . where d cannot equal 0

Then:

(4(a/b) + 7(c/d)) / 6(c/d)

Wouldn't this last statement be a proof in it self since I have expressed (4x + 7y) / 6y as a ratio of two integers, namely 4(a/b) + 7(c/d) and 6(c/d), where 6(c/d) cannot equal 0? Doesn't this show that (4x + 7y) / 6y is rational?

Thanks for any suggestions or pointers to similar problems.