IMC 2008 — Keystage 3 (IWYMIC) — individual Question 3

Positive $a,b,c$ satisfy $a+b+c=11$ and $\frac1{b+c}+\frac1{c+a}+\frac1{a+b}=\frac{13}{17}$. Find $\frac a{b+c}+\frac b{c+a}+\frac c{a+b}$.