Which expression is equivalent to (y +12)/(x−8) + (y(x−8))/(x^2 y−8xy)?
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice C is correct. Factoring the denominator in the second term of the given expression gives y + - 1 8 2 +y^x - - 8 8h. This expression can be rewritten with common denominators by m x ultiply x in y^ g x the h first term by xy , giving xy^y + - 1 8 2 h+y^x - - 8 8h. Adding +12+ -8 xy xy^x h xy^x h these two terms yields xy^y h -8 y^x h. Using the distributive property to rewrite xy^x h 2+12 + -8 xy xy xy y this expression gives 2 -8 . Combining the like terms in the numerator x y xy 2+13 -8 xy xy y of this expression gives 2 -8 . x y xy 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.
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