1966 AHSME Problems/Problem 33

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Problem

If $ab \ne 0$ and $|a| \ne |b|$, the number of distinct values of $x$ satisfying the equation

\[\frac{x-a}{b}+\frac{x-b}{a}=\frac{b}{x-a}+\frac{a}{x-b},\]

is:

$\text{(A) zero}  \quad \text{(B) one}  \quad \text{(C) two}  \quad \text{(D) three}  \quad \text{(E) four}$

Solution

See also

1966 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 32
Followed by
Problem 34
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