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AMC 12/AHSME
1966 AMC 12/AHSME
33
Number of Values that Satisfy the Equation
Number of Values that Satisfy the Equation
Source: 1966 AHSME #33
August 31, 2011
AMC
Problem Statement
If
a
b
≠
0
ab\ne0
ab
=
0
and
∣
a
∣
≠
∣
b
∣
|a|\ne|b|
∣
a
∣
=
∣
b
∣
the number of distinct values of
x
x
x
satisfying the equation
x
−
a
b
+
x
−
b
a
=
b
x
−
a
+
a
x
−
b
\dfrac{x-a}{b}+\dfrac{x-b}{a}=\dfrac{b}{x-a}+\dfrac{a}{x-b}
b
x
−
a
+
a
x
−
b
=
x
−
a
b
+
x
−
b
a
is:
(A) zero
(B) one
(C) two
(D) three
(E) four
\text{(A)}\ \text{zero}\qquad \text{(B)}\ \text{one}\qquad \text{(C)}\ \text{two}\qquad \text{(D)}\ \text{three}\qquad \text{(E)}\ \text{four}
(A)
zero
(B)
one
(C)
two
(D)
three
(E)
four
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