A Sum That Rearranges

If $a,\ b,\ c \in \mathbb{R}^+$ such that $a+b+c = 10$ and $$\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{a+c}= \frac{4}{5}$$determine the value of $$\frac{c}{a+b}+\frac{a}{b+c}+\frac{b}{c+a}$$