For real numbers $a,b,c$ calculate the value of: $\frac{c}{a+b}+\frac{a}{b+c}+\frac{b}{c+a}$ if we have... For real numbers $a,b,c$ we have: $a+b+c=11$ and  $\frac1{a+b}+\frac1{b+c}+\frac1{c+a}=\frac{13}{17}$, calculate the value of: $\frac{c}{a+b}+\frac{a}{b+c}+\frac{b}{c+a}$
I think we should use a trick to solve this,because doing algebraic operations on this problem are too tedius!

$$\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=\frac{a+b+c}{b+c}+\frac{a+b+c}{a+c}+\frac{a+b+c}{a+b}-3=$$
$$=(a+b+c)\left(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{a+c} \right)-3=$$
$$=11\cdot\frac{13}{17}-3=\frac{92}{17}$$
