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Let $f(x) = \left\{ \begin{array}{ll} \frac{x^2-x-2}{x-2} & \mbox{if } x \neq 2 \\ a & \mbox{if } x = 2. \end{array} \right.$ If $f(x)$ is continuous for all real values of $x,$ what is $a?$

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