#inequalities

Prove that for positive real numbers $x_1,\dots ,x_n$ $\frac{x_1+\cdots +x_n}{n}\ge \sqrt[n]{x_1{x}_2\cdots x_n},$ with equality only when all the $x_i$ are equal.

Prove that for all positive real numbers $a$, $b$ and $c$ $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge \frac{3}{2}.$ When does equality hold?