The equation above is true for all , where r and t are positive constants. What is the value of

Question

The equation above is true for all , where r and t are positive constants. What is the value of rt ?

Accepted Answer

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.

Question the-eq