# Math Help - Group Theory - Prove that for ab-cd=1, there is no cancellation for (a+c)/(b+d)

1. ## Group Theory - Prove that for ab-cd=1, there is no cancellation for (a+c)/(b+d)

Hi, I have the following problem.

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

ab-cd=1,

no cancellation is possible in the fraction

(a+c)/(b+d) (where the result of the fraction is a rational number."

Well, I know how to cancel a fraction, but how am I supposed to do this one, and what letters should I use to prove the cancellation?

I'd really appreciate it if you could give me a hand, thanks.

2. A fraction cannot be canceled if the numerator and denominator have GCD 1. Can you show that $\gcd(a+c,b+d)=1$?