Hello!!

Could you please help me with these two exercises

1.- Let $\displaystyle a,b,c $ be real positive numbers and $\displaystyle abc = 1$

Prove that: $\displaystyle \displaystyle\frac{a}{(a+1)(b+1)} + \displaystyle\frac{b}{(b+1)(c+1)} + \displaystyle\frac{c}{(a+1)(c+1)} \geq{\displaystyle\frac{3}{4}}$

Hint: $\displaystyle \sqrt[ ]{xy} \leq{\displaystyle\frac{x+y}{2}}$

2.- Let $\displaystyle a,b,c $ be real positive numbers and $\displaystyle a+b+c = 1$

Prove that: $\displaystyle (\displaystyle\frac{1}{b} + 1)$ $\displaystyle (\displaystyle\frac{1}{b} + 1)$ $\displaystyle (\displaystyle\frac{1}{c} + 1)$ $\displaystyle \geq{64}$

Thanks a lot!!