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Equivalent expressions SAT question
Math · Advanced Math · Hard · Answer it here, explanation included.
The equation above is true for all 
, where r and t are positive constants. What is the value of rt ?
ExplanationShow
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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