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2021 AMC 12B Question 3

AMC12 · 2021 AMC 12B

Question 3

Suppose $$
2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{2}{3+x}}}=\dfrac{144}{53}.
$$

What is the value of $x?$
  1. $\dfrac{3}{4}$
  2. $\dfrac{7}{8}$
  3. $\dfrac{14}{15}$
  4. $\dfrac{37}{38}$
  5. $\dfrac{52}{53}$