Hi,

I have the following problem, but I don't know what to do. I have been told by someone to think about gcd(a+c, b+d), but I still don't know how to prove this. Thanks for your help!

"Prove that for any positive integers a, b, c, d satisfying

$\displaystyle ab-cd=1$

no cancellation is possible in the fraction

$\displaystyle (a+c)/(b+d)$, where the result is a rational number."