{"id":"cb_practice_pdf:t8-math-m2-q26","source_id":"cb_practice_pdf","source_item_id":"t8-math-m2-q26","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-8","module_number":2,"position":26,"stem":"(x^2)/(x^2 −c^2) = (c^2)/(x^2 −c^2) +39 In the given equation, c is a positive constant. Which of the following is one of the solutions to the given equation? −c","stimulus":"","stimulus_html":null,"stem_html":"<p>(x^2)/(x^2 −c^2) = (c^2)/(x^2 −c^2) +39 In the given equation, c is a positive constant. Which of the following is one of the solutions to the given equation? −c</p>","rationale_html":"<p>2- 2#0 Choice D is correct. If x c , then neither side of the given equation is 2- 2&gt;0 c2 defined and there can be no solution. Therefore, x c . Subtracting x2- c2 x 2 - c 2 =39 x 2- c 2 =39 from both sides of the given equation yields 2- 2 2- 2 , or 2- 2 . x c x c x c Squaring both sides of this equation yields e x 2 2 - - c 2 2o 2 =392 , or ^x 2- c 2 2 h - ^x 2 2 - c 2 h=392 . x c x c 2- 2 x2- c2 Since x c is positive and, therefore, nonzero, the expression is defined x2- c2 and equivalent to 1. It follows that the equation ^x 2- c 2 2 h - ^x 2 2 - c 2 h=392 can be rewritten x c x 2- c 2 2- 2 =392 1 2- 2 =392 2- 2=392 as e 2- 2o`x c j , or ^ h^x c h , which is equivalent to x c . x c 2 2= 2+392 Adding c to both sides of this equation yields x c . Taking the square = 2+392 root of both sides of this equation yields two solutions: x c and =- 2+392 - 2+392 x c . Therefore, of the given choices, c is one of the solutions to the given equation. 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.</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>−c^2 −39^2</p>","ord":0},{"label":"B","content_html":"<p>− ✓^39^2 −c^2</p>","ord":1},{"label":"C","content_html":"<p>− ✓,---- c^2 +39^2</p>","ord":2},{"label":"D","content_html":"<p>STO</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}