OG详解-OG7 数学1 Q39

Choice D is correct. Adding 2​t​ to each side of the given equation yields 12n​= -2w​+2t​​. The fractions on the right side of this equation have a common
denominator of tw; therefore, the equation can be written as 12n​=2wtw​+2ttw​​ , or 12n​=2w−2t​tw​, which is equivalent to 12n​=2(w−t)​tw​ . Dividing each side of this equation by 2 yields  6n​=​w−ttw​. Since n, t, w, and w-t are all positive quantities, taking the reciprocal of each side of the equation 6n​=​w−ttw​ yields an equivalent equation 6n​=​w−ttw​. Multiplying each side of this equation by 6 yields n = 6tww−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. Choice C is incorrect. This is equivalent to 1​n​ rather than n.