If a , b and c are three positf real numbers and :
\(\displaystyle
x=\frac{a}{a+b}
\)
\(\displaystyle
y=\frac{b}{b+c}
\)
\(\displaystyle
z=\frac{c}{c+a}
\)
Prove that : \(\displaystyle x+y+z> 1\)

If a , b and c are three positf real numbers and :
\(\displaystyle
x=\frac{a}{a+b}
\)
\(\displaystyle
y=\frac{b}{b+c}
\)
\(\displaystyle
z=\frac{c}{c+a}
\)
Prove that : \(\displaystyle x+y+z> 1\)