{"@context":"https://schema.org/","@type":"Quiz","name":"

Which expression is equivalent to $\\dfrac{y+12}{x-8}+\\dfrac{y(x-8)}{x^{2}y-8xy}$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-144"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

Which expression is equivalent to $\\dfrac{y+12}{x-8}+\\dfrac{y(x-8)}{x^{2}y-8xy}$?

","comment":{"@type":"Comment","text":"

Choice C is correct. Factoring the denominator in the second term of the given expression gives $\\dfrac{y+12}{x-8}+\\dfrac{y(x-8)}{xy(x-8)}$. This expression can be rewritten with common denominators by multiplying the first term by $\\dfrac{xy}{xy}$, giving $\\dfrac{xy(y+12)}{xy(x-8)}+\\dfrac{y(x-8)}{xy(x-8)}$. Adding these two terms yields $\\dfrac{xy(y+12)+y(x-8)}{xy(x-8)}$. Using the distributive property to rewrite this expression gives $\\dfrac{xy^{2}+12xy+xy-8y}{x^{2}y-8xy}$. Combining the like terms in the numerator of this expression gives $\\dfrac{xy^{2}+13xy-8y}{x^{2}y-8xy}$.

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.

"},"encodingFormat":"text/markdown","text":"

Which expression is equivalent to $\\dfrac{y+12}{x-8}+\\dfrac{y(x-8)}{x^{2}y-8xy}$?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$\\dfrac{xy+y+4}{x^{3}y-16x^{2}y+64xy}$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$\\dfrac{xy+9y+12}{x^{2}y-8xy+x-8}$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$\\dfrac{xy^{2}+13xy-8y}{x^{3}y-16x^{2}y+64xy}$

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$\\dfrac{xy^{2}+13xy-8y}{x^{2}y-8xy}$

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-144"}

Which expression is equivalent to $\dfrac{y+12}{x-8}+\dfrac{y(x-8)}{x^{2}y-8xy}$?