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MathNet 2021 — Part 08 Question 74

Math Olympiad Vault · MathNet 2021 — Part 08

Question 74

Let $x\in\mathbb R$ satisfy $x\gt0$, $x\ne4$ and $x\ne9$. Which expression is equivalent to $\left((2+\sqrt{x})^{-1}+1\right)^{-1}$?
  1. $\frac{x+\sqrt{x}-6}{x-9}$
  2. $\frac{x-\sqrt{x}-6}{x-9}$
  3. $\frac{x-\sqrt{x}+6}{x-9}$
  4. $\frac{x-\sqrt{x}-6}{x-4}$
  5. $\frac{x-\sqrt{x}+6}{x-4}$