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

Which expression is equivalent to $\\frac{4}{4x-5} - \\frac{1}{x+1}$?

","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-36"}],"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 $\\frac{4}{4x-5} - \\frac{1}{x+1}$?

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

Choice D is correct. The expression $\\frac{4}{4x-5}-\\frac{1}{x+1}$ can be rewritten as $\\frac{4}{4x-5}+\\frac{(-1)}{x+1}$. To add the two terms of this expression, the terms can be rewritten with a common denominator. Since $\\frac{x+1}{x+1}=1$, the expression $\\frac{4}{4x-5}$ can be rewritten as $\\frac{(x+1)(4)}{(x+1)(4x-5)}$. Since $\\frac{4x-5}{4x-5}=1$, the expression $\\frac{-1}{x+1}$ can be rewritten as $\\frac{(4x-5)(-1)}{(4x-5)(x+1)}$. Therefore, the expression $\\frac{4}{4x-5}+\\frac{(-1)}{x+1}$ can be rewritten as $\\frac{(x+1)(4)}{(x+1)(4x-5)}+\\frac{(4x-5)(-1)}{(4x-5)(x+1)}$, which is equivalent to $\\frac{(x+1)(4)+(4x-5)(-1)}{(x+1)(4x-5)}$. Applying the distributive property to each term of the numerator yields $\\frac{(4x+4)+(-4x+5)}{(x+1)(4x-5)}$, or $\\frac{(4x+(-4x))+(4+5)}{(x+1)(4x-5)}$. Adding like terms in the numerator yields $\\frac{9}{(x+1)(4x-5)}$.

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 and may result from conceptual or calculation errors.

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Which expression is equivalent to $\\frac{4}{4x-5} - \\frac{1}{x+1}$?

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

$\\frac{1}{(x+1)(4x-5)}$

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

$\\frac{3}{3x-6}$

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

$-\\frac{1}{(x+1)(4x-5)}$

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

$\\frac{9}{(x+1)(4x-5)}$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-36"}

Which expression is equivalent to $\frac{4}{4x-5} - \frac{1}{x+1}$?