Prove the inequality $\frac{a^2+1}{b+c}+\frac{b^2+1}{a+c}+\frac{c^2+1}{a+b}\ge 3$ 
If $a,b,c\in\mathbb R^+$ prove that:
   $$\frac{a^2+1}{b+c}+\frac{b^2+1}{a+c}+\frac{c^2+1}{a+b}\ge 3$$


Apply Am-GM to the numerator of each fraction. 
You get the statement of Nesbit inequality. 
