[HELP]Relative Primality in the Following Algorithm

Hi all,

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

greatly appreciated.

// 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.