{"id":"cb_question_bank:626c66ad-8ea0-4df4-9dbd-ea8aff9020fe","source_id":"cb_question_bank","source_item_id":"626c66ad-8ea0-4df4-9dbd-ea8aff9020fe","external_id":null,"ibn":"09413-DC","question_id":"22fd3e1f","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":"Which of the following expressions is equivalent to the fraction f of x over g of x , for x is greater than 3 ?","stimulus":"f of x equals, x cubed minus, 9 x, and, g of x equals, x squared minus, 2 x minus 3","stimulus_html":"<div class=\"stimulus_reference \">\n\t<p class=\"standalone_statement style:1 \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0d3dc7d32dc667ca84d38b118615e6e0910fcf747c890f19852cc68e5dea539c\" alt=\"f of x equals, x cubed minus, 9 x, and, g of x equals, x squared minus, 2 x minus 3 \"></span></span></p>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following expressions is equivalent to <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f7b33844370f4611dcc68eb2e5fb277c16c27aa99c583ac012b293f3e8cbb614\" alt=\"the fraction f of x over g of x\"></span></span>, for <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/01f9d23462be7959a598b9a2f69e5115fcfbc0ffbd94270bd39b801dfa72043c\" alt=\"x is greater than 3\"></span></span>&nbsp;?</p>\n","rationale_html":"<p>Choice D is correct. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/78ae7931ac8191bbe1488423a3f3247649158ede6c1896ada15b34c076552eab\" alt=\"x cubed, minus 9 x, equals, x times, open parenthesis, x plus 3, close parenthesis, times, open parenthesis, x minus 3, close parenthesis\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d33c002a4a25b5497dcac27dc7a54b8e7f8ba1f4c69ce177d56e52cc0e155a6e\" alt=\"x squared, minus 2 x, minus 3, equals, open parenthesis, x plus 1, close parenthesis, times, open parenthesis, x minus 3, close parenthesis\"></span>, the fraction<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f7b33844370f4611dcc68eb2e5fb277c16c27aa99c583ac012b293f3e8cbb614\" alt=\"f of x, over g of x\"></span> can be written as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c94fce97757f784221a872bbc1d1ba2f179fb435d854c68ec2e2663fd2de2830\" alt=\"the fraction with numerator x times, open parenthesis, x plus 3, close parenthesis, times, open parenthesis, x minus 3, close parenthesis, and denominator, open parenthesis, x plus 1, close parenthesis, times, open parenthesis, x minus 3, close parenthesis, end fraction\"></span>. It is given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e63c9fc926c9432310e7e5b36b91facce36c2447501202f3ea592564860fe64\" alt=\"x is greater than 3\"></span>, so the common factor <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d9271eeef645afaa9ab7c8ad232ff3aed82b616a589370d0281402c0c71b76dd\" alt=\"x minus 3\"></span> is not equal to 0. Therefore, the fraction can be further simplified to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1257c2d629737309b92e8834f318814ae32766e5e1b903873538cabc4a8b4f59\" alt=\"the fraction with numerator x times, open parenthesis, x plus 3, close parenthesis, and denominator x plus 1, end fraction\"></span>.</p><p>Choice A is incorrect. The expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/94f749e179fbf3e8e288ef6ae3ed29f86b2254e15721a1c43430a3b03791b95a\" alt=\"the fraction 1 over, x plus 1, end fraction\"></span> is not equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f7b33844370f4611dcc68eb2e5fb277c16c27aa99c583ac012b293f3e8cbb614\" alt=\"the fraction f of x, over g of x\"></span> because at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/94f749e179fbf3e8e288ef6ae3ed29f86b2254e15721a1c43430a3b03791b95a\" alt=\"the fraction 1 over, x plus 1, end fraction\"></span> as a value of 1 and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f7b33844370f4611dcc68eb2e5fb277c16c27aa99c583ac012b293f3e8cbb614\" alt=\"the fraction f of x, over g of x\"></span> has a value of 0.</p><p>Choice B is incorrect and results from omitting the factor <span class=\"italic\">x</span> in the factorization of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/26d9f477bb154c8ef7637e64827776ac5831aa760a31d21a53157367bd210b16\" alt=\"f of x\"></span>. Choice C is incorrect and may result from incorrectly factoring <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e73c4143337b0e2b667e806f5a9a61b4acf325e1a2280e45cbc73be42bfab17f\" alt=\"g of x\"></span> as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ae5e9c6da0caffc770a5e61becf997978a03fd38a36aee16eae39ac164e9914a\" alt=\"open parenthesis, x plus 1, close parenthesis, times, open parenthesis, x plus 3, close parenthesis\"></span> instead of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bbf799455119d89fcc5502e410f15ee938207d2c5204315794ffe52e4491ba08\" alt=\"open parenthesis, x plus 1, close parenthesis, times, open parenthesis, x minus 3, close parenthesis\"></span>.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+00:00","options":[{"label":"A","content_html":"<p><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/94f749e179fbf3e8e288ef6ae3ed29f86b2254e15721a1c43430a3b03791b95a\" alt=\"the fraction with numerator 1, and denominator x plus 1, end fraction\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e272d677128d6be219ae0a9030080c8c77c2ed5597ded74a91e1ece8448ecb0b\" alt=\"the fraction with numerator x plus 3, and denominator x plus 1, end fraction\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b37a050cab67b3edc3a8570ae1a889f71e6cf6fb28a0692409075e768134e2c2\" alt=\"the fraction with numerator x times, open parenthesis, x minus 3, close parenthesis, and denominator x plus 1, end fraction\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1257c2d629737309b92e8834f318814ae32766e5e1b903873538cabc4a8b4f59\" alt=\"the fraction with numerator x times, open parenthesis, x plus 3, close parenthesis, and denominator x plus 1, end fraction\"></span></span></p>\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}}