<s>[INST] 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!
 [/INST] Hint:
As $(a+b+c) ( \frac1{a+b}+\frac1{b+c}+\frac1{c+a})= 3+\frac{a}{b+c} +\frac{b}{c+a} + \frac{c}{a+b}$

Now applying the values given in question we get $\frac{a}{b+c} +\frac{b}{c+a} + \frac{c}{a+b}=(11 \cdot \frac{13}{17})- 3=\frac{92}{17}$
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