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.
x = a/b . . . where b cannot equal 0
y = c/d . . . where d cannot equal 0
(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.