\(A=\dfrac{a^2}{a+b}+\dfrac{b^2}{b+c}+\dfrac{c^2}{c+a}-\dfrac{b^2}{a+b}-\dfrac{c^2}{b+c}-\dfrac{a^2}{a+c}\)
\(A=\left(\dfrac{a^2}{a+b}-\dfrac{b^2}{a+b}\right)+\left(\dfrac{b^2}{b+c}-\dfrac{c^2}{b+c}\right)+\left(\dfrac{c^2}{c+a}-\dfrac{a^2}{c+a}\right)\)
\(A=\dfrac{\left(a-b\right)\left(a+b\right)}{a+b}+\dfrac{\left(b-c\right)\left(b+c\right)}{b+c}+\dfrac{\left(c-a\right)\left(c+a\right)}{c+a}\)
\(A=a-b+b-c+c-a\left(\text{Đ}K:\left\{{}\begin{matrix}a+b\ne0\\b+c\ne0\\c+a\ne0\end{matrix}\right.\right)\)
\(A=0\)
Vậy \(A=0\)
Tham khảo nhé~
\(A=\dfrac{a^2}{a+b}+\dfrac{b^2}{b+c}+\dfrac{c^2}{c+a}-\dfrac{b^2}{a+b}-\dfrac{c^2}{b+c}-\dfrac{a^2}{c+a}\)
\(\Leftrightarrow A=\dfrac{a^2-b^2}{a+b}+\dfrac{b^2-c^2}{b+c}+\dfrac{c^2-a^2}{c+a}\)
\(\Leftrightarrow A=\dfrac{\left(a-b\right)\left(a+b\right)}{\left(a+b\right)}+\dfrac{\left(b-c\right)\left(b+c\right)}{\left(b+c\right)}+\dfrac{\left(c-a\right)\left(c+a\right)}{c+a}\)
\(\Leftrightarrow A=a-b+b-c+c-a\)
\(\Leftrightarrow A=0\)