Mathematics Olympiad Question $a+b+c=7$, ... Given $a+b+c=7$ and $\frac{1}{a+b} + \frac{1}{b+c} + \frac{1}{c+a} = 0.7$, need to find $\frac{c}{a+b} + \frac{a}{b+c} + \frac{b}{a+c}$.
I have noted that these two differ by a factor of $10$. So I divided the first equation by $10$ and equated the two. But that did not lead me anywhere. I have also tried to multiply one by the other, but the result obtained is identical to just multiplying the second expression by $7$.

$$\frac{c}{a+b}+\frac{a}{b+c}+\frac{b}{a+c}$$
$$=\frac{7-(a+b)}{a+b}+\frac{7-(b+c)}{b+c}+\frac{7-(a+c)}{a+c}$$
$$=\frac{7}{a+b}+\frac{7}{b+c}+\frac{7}{a+c}-3$$
$$=7\cdot 0.7-3=1.9$$
