OG详解-OG9 数学2 Q25

Choice C is correct. Factoring the denominator in the second term of the given expression gives y+12x−8​+y(x−8)xy(x−8​)​ . This expression can be rewritten with common denominators by multiplying the first term by xyxy​​ , giving xy(y+12)xy(x−8)​+y(x−8)xy(x−8​)​ .Adding these two terms yields xy(y+12)+y(x−8​)xy(x−8)​ . Using the distributive property to rewrite this expression gives xy2+12xy+xy−8yx2y−8xy​​ . Combining the like terms in the numerator of this expression gives xy2+13​xy−8yx2y−8xy​ .
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 D is incorrect and may result from conceptual or calculation errors.