{"id":"cb_question_bank:24709753-58b0-4689-b7bf-2853ad32f70e","source_id":"cb_question_bank","source_item_id":"24709753-58b0-4689-b7bf-2853ad32f70e","external_id":null,"ibn":"022991-DC","question_id":"34847f8a","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The equation above is true for all x greater than 2 , where r and t are positive constants. What is the value of rt ?","stimulus":"the fraction with numerator 2, and denominator x minus 2, end fraction, plus, the fraction with numerator 3, and denominator x plus 5, end fraction, equals, the fraction with numerator r x plus t, and denominator, open parenthesis, x minus 2, close parenthesis, times, open parenthesis, x plus 5, close parenthesis, end fraction","stimulus_html":"
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\n \n \"the\n

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The equation above is true for all \"x, where r and t are positive constants. What is the value of rt ?

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Choice C is correct. To express the sum of the two rational expressions on the left-hand side of the equation as the single rational expression on the right-hand side of the equation, the expressions on the left-hand side must have the same denominator. Multiplying the first expression by \"the results in \"the, and multiplying the second expression by \"the results in \"the, so the given equation can be rewritten as \"the, or \"the. Since the two rational expressions on the left-hand side of the equation have the same denominator as the rational expression on the right-hand side of the equation, it follows that \"open. Combining like terms on the left-hand side yields \"5, so it follows that \"r and \"t. Therefore, the value of \"r is \"5.

Choice A is incorrect and may result from an error when determining the sign of either r or t. Choice B is incorrect and may result from not distributing the 2 and 3 to their respective terms in \"the. Choice D is incorrect and may result from a calculation error.

\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.618000+00:00","source_updated_at":"2023-08-02T20:25:59.618000+00:00","options":[{"label":"A","content_html":"\"negative\n","ord":0},{"label":"B","content_html":"\"15\"\n","ord":1},{"label":"C","content_html":"\"20\"\n","ord":2},{"label":"D","content_html":"\"60\"\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}