number theory - Prove that $gcd(m+m', n+n') = 1$

I'm stuck trying to solve this problem:

"Given positive integers $m, n, m', n'$ such as $m/n < m'/n'$ and $m'n - mn' = 1$, we define $$a/b = (m+m')/(n+n').$$ Check that $m/n < a/b < m'/n'$ and prove that $$gcd(a, b) = 1."$$

The way I see it, it must be that $a = m+m'$ and $b = n+n'$. But I'm not sure how to prove the $gcd(a,b) = 1$ part. Any help would be appreciated.

Answer

Hint: $\ (m+m')\,n - m\,(n'+n) = m'n-mn'= 1$,