AHSME 1968 Problem 4

Define an operation $\star$ for positive real numbers as $a\star b=\frac{ab}{a+b}$. Then $4 \star (4 \star 4)$ equals: $\text{(A) } \frac{3}{4} \text{(B) } 1 \text{(C) } \frac{4}{3} \text{(D) } 2 \text{(E )} \frac{16}{3}$