N5

Part of JOM 2015 Shortlist

Problems(1)

\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b}

Source: Junior Olympiad of Malaysia Shortlist 2015 N5

a,b,c

be pairwise coprime positive integers. Find all positive integer values of

\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b}