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1966 AMC 12 Question 33

AMC12 · 1966 AMC 12

Question 33

If $ab\ne0$ and $|a|\ne|b|,$ the number of distinct values of $x$ satisfying the equation

$$
\begin{aligned} \frac{x-a}{b}+\frac{x-b}{a} &=\frac{b}{x-a}\\ &\quad+\frac{a}{x-b} \end{aligned}
$$

is:
  1. $0$
  2. $1$
  3. $2$
  4. $3$
  5. $4$