<p>Define an operation <img alt="$\star$" height="10" src="https://latex.artofproblemsolving.com/d/1/7/d17950ad2ab63c764778b133f95a03dcf2969d57.png" width="11" /> for positive real numbers as <img alt="$a\star b=\frac{ab}{a+b}$" height="39" src="https://latex.artofproblemsolving.com/0/f/f/0ff3c1f09b31819086f62acf5ea68a90e93f3ea4.png" width="101" />. Then <img alt="$4 \star (4 \star 4)$" height="18" src="https://latex.artofproblemsolving.com/2/5/e/25ee6fe35a3ce297d5238e1f885f50961ed32114.png" width="74" /> equals:</p> <p><img alt="$\text{(A) } \frac{3}{4}\quad \text{(B) } 1\quad \text{(C) } \frac{4}{3}\quad \text{(D) } 2\quad \text{(E )} \frac{16}{3}$" height="38" src="https://latex.artofproblemsolving.com/c/0/0/c000bc37638a61938500f347e0c3ab4292fc34af.png" width="283" /></p>

Question No: 479

Define an operation $\star$ for positive real numbers as $a\star b=\frac{ab}{a+b}$ . Then $4 \star (4 \star 4)$ equals:

$\text{(A) } \frac{3}{4}\quad \text{(B) } 1\quad \text{(C) } \frac{4}{3}\quad \text{(D) } 2\quad \text{(E )} \frac{16}{3}$

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Tags: Algebra

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