The equation above is true for all , where r and t are positive constants. What is the value of rt ?
-
A
-
B
-
C
-
D
Correct answer: C
Explanation
Choice C is correct. To express the sum of the two rational expressions on the left-hand side of the equation as the single rational expression on the right-hand side of the equation, the expressions on the left-hand side must have the same denominator. Multiplying the first expression by results in
, and multiplying the second expression by
results in
, so the given equation can be rewritten as
, or
. Since the two rational expressions on the left-hand side of the equation have the same denominator as the rational expression on the right-hand side of the equation, it follows that
. Combining like terms on the left-hand side yields
, so it follows that
and
. Therefore, the value of
is
.
Choice A is incorrect and may result from an error when determining the sign of either r or t. Choice B is incorrect and may result from not distributing the 2 and 3 to their respective terms in . Choice D is incorrect and may result from a calculation error.
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