CEMC Fermat, 1999

Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

If $a_1 = \frac{1}{1-x}$ , $a_2 = \frac{1}{1-a_1}$ , and $a_n = \frac{1}{1-a_{n-1}}$ , for $n \ge 2$ , $x \ne 1$ and $x \ne 0$ , then $a_{107}$ is

(A) $\frac{1}{1-x}$ (B) $x$ (C) $-x$ (D) $\frac{x-1}{x}$ (E) $\frac{1}{x}$

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