{"id":"informator-maturalny-matematyka-2010/zad/60","paper_id":"informator-maturalny-matematyka-2010","number":"60","points":2,"ptype":"open","subject":"matematyka","category":"informator-maturalny","year":2010,"month":null,"level":null,"text":"Zadanie 60. (2 pkt)\nWyrażenie\n3\n3\n1\nx\nx\nx\n+ zapisz w postaci ilorazu dwóch wielomianów.","answer":null,"answer_text":null,"solution":"3/(x-3) - x/(x+1), wspólny mianownik (x-3)(x+1):\n= [3(x+1) - x(x-3)] / [(x-3)(x+1)]\n= [3x+3 - x^2+3x] / [(x-3)(x+1)]\n= (-x^2+6x+3) / (x^2-2x-3).\nOdpowiedź: (-x^2+6x+3)/(x^2-2x-3), czyli równoważnie -(x^2-6x-3)/((x-3)(x+1)).","image":"img/informator-maturalny-matematyka-2010/zad-60.webp","solution_image":null,"topics":null,"page_from":84,"source":"ai","answer_source":null,"answer_text_source":null,"solution_source":"ai","text_source":"ocr","source_label":"Matematyka · Informator maturalny · 2010","subject_label":"Matematyka","category_label":"Informator maturalny","text_html":"<p>Zadanie 60. (2 pkt)<br>Wyrażenie<br>3<br>3<br>1<br>x<br>x<br>x</p>\n<ul><li>zapisz w postaci ilorazu dwóch wielomianów.</li></ul>","solutions":[{"source":"ai","label":"AI","kind":"text","html":"<p>3/(x-3) - x/(x+1), wspólny mianownik (x-3)(x+1):<br>= [3(x+1) - x(x-3)] / [(x-3)(x+1)]<br>= [3x+3 - x^2+3x] / [(x-3)(x+1)]<br>= (-x^2+6x+3) / (x^2-2x-3).<br>Odpowiedź: (-x^2+6x+3)/(x^2-2x-3), czyli równoważnie -(x^2-6x-3)/((x-3)(x+1)).</p>"}]}