AMC 12B 2021 Spring Problem 3

Past Contests AMC 12 AMC 12B - 2021 (Spring)
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1

Suppose

2+\dfrac{1}{1+\dfrac{1}{2+\dfrac{2}{3+x}}}=\dfrac{144}{53}

What is the value of x ?

Answer Choices
A. \dfrac{3}{4}
B. \dfrac{7}{8}
C. \dfrac{14}{15}
D. \dfrac{37}{38}
E. \dfrac{52}{53}