{"id":"aqua_rat:7289a37cab0a30554e8cb694a5f3629b","source_id":"aqua_rat","source_item_id":"7289a37cab0a30554e8cb694a5f3629b","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"The root(s) of 15/(x2 - 4) – 2/(x - 2) = 1 is (are):","stimulus":"","stimulus_html":null,"stem_html":"<p>The root(s) of 15/(x2 - 4) – 2/(x - 2) = 1 is (are):</p>","rationale_html":"<p>15/(x2 - 4) – 2/(x - 2) = 1.</p><p>15/(x2 - 22) – 2/(x - 2) = 1.</p><p>15/(x + 2)(x - 2) – 2/(x - 2) = 1.</p><p>[15 – 2(x + 2)]/[(x + 2)(x - 2)] = 1.</p><p>[15 – 2x - 4] /[(x + 2)(x - 2)] = 1.</p><p>[11 - 2x]/[(x + 2)(x - 2)] = 1.</p><p>11 – 2x = (x + 2)(x - 2).</p><p>11 – 2x = x2 - 4.</p><p>x2 - 4 = 11 – 2x.</p><p>x2 + 2x – 4 – 11 = 0.</p><p>x2 + 2x – 15 = 0.</p><p>x + 5) (x - 3) = 0.</p><p>x + 5 = 0 or, x – 3 = 0</p><p>x = -5 or, x = 3.</p><p>Therefore, x = -5 and 3.</p><p>A</p>","correct_answer":["A"],"equiv_key":"6346cbfd88dc93c6ea322b4a","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>-5 and 3</p>","ord":0},{"label":"B","content_html":"<p>± 2</p>","ord":1},{"label":"C","content_html":"<p>2 only</p>","ord":2},{"label":"D","content_html":"<p>-3 and 5</p>","ord":3},{"label":"E","content_html":"<p>3 only.</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}