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12/n − 2/t = − 2/w The given equation relates the variables n, t, and w, > 0 > 0 > where n, t, and w t. Which expression is equivalent to n? 12tw
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
2 Choice D is correct. Adding to each side of the given equation yields 12 2 2 t =- + . The fractions on the right side of this equation have a common n w t 12 2 2 = w- t denominator of tw; therefore, the equation can be written as , or 12 = 2 w -2 t , which is equivalent to 12 = 2 ^w - th. Dividing each si n de o t f w this t w equation n tw n tw 6=w - t - by 2 yields . Since n, t, w, and w t are all positive quantities, taking the n tw 6=w - t reciprocal of each side of the equation yields an equivalent equation: n tw n= tw =6tw - . Multiplying each side of this equation by 6 yields n - . 6 w t w t Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. 1 Choice C is incorrect. This is equivalent to rather than n. n
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