\(\dfrac{x^2-z^2}{y+z}+\dfrac{y^2-x^2}{z+x}+\dfrac{z^2-y^2}{x+y}\ge0\)

\(\Leftrightarrow\dfrac{x^4+y^4+z^4-x^2y^2-y^2z^2-x^2z^2}{\left(x+y\right)\left(x+z\right)\left(y+z\right)}\ge0\)

\(\Leftrightarrow\dfrac{\left(x^4-2x^2y^2+y^4\right)+\left(y^4-2y^2z^2+z^4\right)+\left(z^4-2x^2z^2+x^4\right)}{\left(x+y\right)\left(x+z\right)\left(y+z\right)}\ge0\)

\(\Leftrightarrow\dfrac{\left(x^2-y^2\right)^2+\left(y^2-z^2\right)^2+\left(z^2-x^2\right)^2}{\left(x+y\right)\left(x+z\right)\left(y+z\right)}\ge0\left(\text{*}\right)\)

The last inequality is obvious

\("="\Leftrightarrow x=y=z\)

You can change your avatar in your profile. This page has that function to do that. If there're any problems, go to https://www.facebook.com/mathu and send a message to us. 

I WANT TO KNOW THE REASON WHY I CAN"T CHANGE MY AVATAR ? NEED A CLEARLY EXPLAIN AND WHO KNOW HOW TO CHANGE IT PLS SHARE WITH ME?

FORGIVE ME ABOUT SPAM BUT IT"S REALLY IMPORTANT WITH ME, Tks so much