<p>Define an operation <img alt="$\star$" height="9" src="https://latex.artofproblemsolving.com/d/1/7/d17950ad2ab63c764778b133f95a03dcf2969d57.png" width="9" /> 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>

Question No: 311

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

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Tags: Algebra

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