Define an operation $\star$ for positive real numbers as $a\star b=\frac{ab}{a+b}$. Then $4 \star (4 \star 4)$ equals:
$\text{(A) } \frac{3}{4}\quad \text{(B) } 1\quad \text{(C) } \frac{4}{3}\quad \text{(D) } 2\quad \text{(E )} \frac{16}{3}$
$4 \star 4 \star 4 = 4 \star 2 = \frac{4}{3}$
Therefore, our answer is $\fbox{C}$
Solution by VivekA