[HELP]Relative Primality in the Following Algorithm
I'm studying Number Theory on my own. I'm having difficulty proving
the relative primality of t1 and t2 in the following algorithm. Any suggestion or help will be
// An algorithm that returns the sum of two rational numbers.
SUM(r1 /r2 , s1 /s2 )
d ← gcd(r2 , s2 );
r3← r2 /d;
s3 ← s2 /d;
T1 ← r1s3 + s1r3 ;
e ← gcd(T1 , d);
t1 ← T1 /e;
t2 ← (r2 /e) · s3 ;
return(t1 /t2 );
//gcd stands for greatest common divisor.
Thank you in advance.