\(\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+a}=\frac{b^2}{a+b}+\frac{c^2}{b+c}+\frac{a^2}{c+a}\)
\(\Leftrightarrow\frac{a^2-b^2}{a+b}+\frac{b^2-c^2}{b+c}+\frac{c^2-a^2}{c+a}=0\)
\(\Leftrightarrow\left(a-b\right)+\left(b-c\right)+\left(c-a\right)=0\)
\(\Rightarrowđpcm\)