{"id":"cb_question_bank:bd215896-5637-4396-99f4-e92dcb4dee3a","source_id":"cb_question_bank","source_item_id":"bd215896-5637-4396-99f4-e92dcb4dee3a","external_id":null,"ibn":"05695-DC","question_id":"89fc23af","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"H","score_band":7,"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 with numerator x squared, minus 2 x, minus 5, and denominator x minus 3 ?","stimulus":"","stimulus_html":null,"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/ec58a3784dee2a26f03dc3d6d6c0f2292ed22151a69b70f1c4807cd592cac2c0\" alt=\"the fraction with numerator x squared, minus 2 x, minus 5, and denominator x minus 3\"></span>&nbsp;</span>?</p>\n","rationale_html":"<p>Choice D is correct. The numerator of the given expression can be rewritten in terms of the denominator, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d9271eeef645afaa9ab7c8ad232ff3aed82b616a589370d0281402c0c71b76dd\" alt=\"x minus 3\"></span>, as follows: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3c64992200c147f01de521ffaa4f5522182bf64a05fbb73df9ae27f0aaed6f0b\" alt=\"x squared, minus 2 x, minus 5, equals, x squared, minus 3 x, plus x, minus 3, minus 2\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/959ef38b6c331f2563a6c4ea2a33b65dbde3624ece3377c6b081928fa1ab5943\" alt=\"x times, open parenthesis, x minus 3, close parenthesis, plus, open parenthesis, x minus 3, close parenthesis, minus 2\"></span>. So the given expression is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/292096557cb540ed9ed28be8aa191ee33f3037fb36fb7566015309fa9b2c735b\" alt=\"the fraction with numerator x times, open parenthesis, x minus 3, close parenthesis, plus, open parenthesis, x minus 3, close parenthesis, minus 2, and denominator x minus 3, end fraction, equals, the fraction with numerator x times, open parenthesis, x minus 3, close parenthesis, and denominator x minus 3, end fraction, plus the fraction with numerator x minus 3, and denominator x minus 3, end fraction, minus the fraction with numerator 2, and denominator x minus 3, end fraction\"></span>. Since the given expression is defined for <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fba6d5f09d883a9cac6d006ecc7de9323aec900c3a00375cfb6556d74006d280\" alt=\"x is not equal to 3\"></span>, the expression can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4821ecff78e4f1ace2df4110ed0bced8f86b3397caaf4ff2c3079c8cc957a5bf\" alt=\"x plus 1, minus, the fraction with numerator 2, and denominator x minus 3, end fraction\"></span>.</p><p>Long division can also be used as an alternate approach. Choices A, B, and C are incorrect and may result from errors made when dividing the two polynomials or making use of structure.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.629000+00:00","source_updated_at":"2023-08-02T20:25:59.629000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/03ddd70e95374db24ebb59fa93eef306e241c3facfa3647c1ff395f33dcc35f8\" alt=\"x minus 5, minus the fraction with numerator 20, and denominator x minus 3\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/374b9ac94be7f3c6eb8554571df2ad335d82525f6d8f8483592ab8bdc61eb975\" alt=\"x minus 5, minus the fraction with numerator 10, and denominator x minus 3\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2db911faf8b309a1218b9be751536a727c7717e9aecb2570a4d8c654ec88f81d\" alt=\"x plus 1, minus the fraction with numerator 8, and denominator x minus 3\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7682cd5b36d780e3eeac9b3fea2f8ae942ae97a5f62f0cd65948aae24d5dbbf7\" alt=\"x plus 1, minus the fraction with numerator 2, and denominator x minus 3\"></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}}