Given a+b+c=0 , prove

\dfrac{a^2}{2a^2+bc}+\dfrac{b^2}{2b^2+ac}+\dfrac{c^2}{2c^2+ab}

Given a+b+c=0 , abc ≠ 0 , a, b,c, are not equal to each other, find the value of a(\dfrac{1}{b}+\dfrac{1}{c})+b(\dfrac{1}{c}+\dfrac{1}{a})+c(\dfrac{1}{a}+\dfrac{1}{b})

If a+b+c=0 , \dfrac{b-c}{a}+\dfrac{c-a}{b}+\dfrac{a-b}{c}=0 , prove \dfrac{bc+b-c}{b^2c^2}+\dfrac{ca+c-a}{c^2a^2}+\dfrac{ab+a-b}{a^2b^2}=0

If real numbers a,b, c satisfy a+b+c=0 , abc=4 , which one best describes the value of

\dfrac{1}{a} +\dfrac{1}{b} +\dfrac{1}{c}

If a, b, c are rational numbers but not zero, a+b+c=0 , what is the value of

\dfrac{1}{b^2+c^2-a^2} +\dfrac{1}{c^2+a^2-b^2} +\dfrac{1}{a^2+b^2-c^2}

Given a+b+c=0 , abc ≠ 0 , a, b,c, are not equal to each other, find the value of

\dfrac{a^2}{bc} +\dfrac{b^2}{ac} +\dfrac{c^2}{ab}