OG详解-OG3 数学1 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 byxy​xy, 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−8y​x2y 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.