{"article_info":{"article_id":141106,"cat_id":1439,"cat_title":"SGK Toán 8 - Cùng khám phá","publish_time":1686388140,"cat_id2":1439,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2023/0610/resize_1-0_69.png","title":"Giải bài 2.15 trang 46 SGK Toán 8 - Cùng khám phá","label":"Giải bài 2.15 trang 46","alias":"giai-bai-215-trang-46-sgk-toan-8-cung-kham-pha","introtext":"Thực hiện các phép tính sau:","content":"<style>\r\n.method-close-icon{position: relative;float: right;top: 6px;transform: rotate(270deg);-ms-transform:rotate(270deg);-moz-transform:rotate(270deg);-webkit-transform:rotate(270deg);-o-transform:rotate(270deg);}\r\n.method-open-icon{position: relative;float: right;top: 6px;}\r\n</style>\r\n<p><strong style=\"font-size: 16px;\">Đề bài</strong></p><p>Thực hiện các phép tính sau:</p>\r\n<p>a) \\(\\frac{1}{{2x - 3}} - \\frac{2}{{3 - 2x}} + \\frac{{18}}{{9 - 4{x^2}}}\\)</p>\r\n<p>b) \\(\\frac{2}{{{a^2} - 1}} - \\frac{1}{{a + 1}} - \\frac{1}{{a - 1}}\\)</p>\r\n<p>c) \\(\\frac{{a + b}}{{a - b}} + \\frac{{{a^2} - 4{b^2}}}{{{a^2} - {b^2}}} - \\frac{{a - 3b}}{{a + b}}\\)</p>\r\n<p>d) \\(\\frac{x}{{{x^2} + xy}} - \\frac{y}{{{x^2} - {y^2}}} + \\frac{{x + y}}{{xy - {y^2}}}\\)</p><div id=\"pos_end_question\"></div><div style=\"padding-top: 10px;padding-bottom: 2px;margin-bottom: 10px;\"><p class=\"show-detail-method\" style=\"background: #654bc2;text-align: center;border-radius:5px;padding: 10px;margin-bottom: 0px;\" onclick=\"showDetailMethod();\"><strong style=\"font-size: 16px;\">Phương pháp giải - Xem chi tiết</strong><img class=\"method-open-icon\" id=\"method_colapse_icon\" src=\"data:image/png;base64,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\"></p>  <div class=\"content_method_content\" style=\"padding: 10px 10px 5px 10px;border: dashed 1px #654bc2;border-top:none;\"><p>Ta quy đồng mẫu thức rồi áp dụng quy tắc cộng, trừ các phân thức có cùng mẫu thức vừa tìm được.</p>  </div>\r\n<script type=\"text/javascript\">\r\n    var is_open =true;\r\n    function showDetailMethod(){\r\n        if(is_open){\r\n            document.querySelector(\".content_method_content\").style.display='none';\r\n            document.getElementById(\"method_colapse_icon\").classList.remove(\"method-open-icon\");\r\n            document.getElementById(\"method_colapse_icon\").classList.add(\"method-close-icon\");\r\n        }else{\r\n            document.querySelector(\".content_method_content\").style.display='block';\r\n            document.getElementById(\"method_colapse_icon\").classList.remove(\"method-close-icon\");\r\n            document.getElementById(\"method_colapse_icon\").classList.add(\"method-open-icon\");\r\n        }\r\n        is_open = !is_open;\r\n    }\r\n</script>\r\n</div><p><strong style=\"font-size: 16px;\">Lời giải chi tiết</strong></p><p>a)</p>\r\n<p>\\(\\begin{array}{l}\\frac{1}{{2x - 3}} - \\frac{2}{{3 - 2x}} + \\frac{{18}}{{9 - 4{x^2}}} = \\frac{{ - \\left( {3 + 2x} \\right) - 2\\left( {3 + 2x} \\right) + 18}}{{9 - 4{x^2}}} = \\frac{{ - 3 - 2x - 6 - 4x + 18}}{{9 - 4{x^2}}}\\\\ = \\frac{{9 - 6x}}{{9 - 4{x^2}}} = \\frac{{3\\left( {3 - 2x} \\right)}}{{\\left( {3 - 2x} \\right)\\left( {3 + 2x} \\right)}} = \\frac{3}{{3 + 2x}}\\end{array}\\)</p>\r\n<p>b)</p>\r\n<p>\\(\\frac{2}{{{a^2} - 1}} - \\frac{1}{{a + 1}} - \\frac{1}{{a - 1}} = \\frac{{2 - \\left( {a - 1} \\right) - \\left( {a + 1} \\right)}}{{\\left( {a - 1} \\right)\\left( {a + 1} \\right)}} = \\frac{{2 - a + 1 - a - 1}}{{\\left( {a - 1} \\right)\\left( {a + 1} \\right)}} = \\frac{{2\\left( {1 - a} \\right)}}{{\\left( {a - 1} \\right)\\left( {a + 1} \\right)}} = \\frac{{ - 2}}{{a + 1}}\\)</p>\r\n<p>c)</p>\r\n<p> \\(\\begin{array}{l}\\frac{{a + b}}{{a - b}} + \\frac{{{a^2} - 4{b^2}}}{{{a^2} - {b^2}}} - \\frac{{a - 3b}}{{a + b}} = \\frac{{{a^2} + 2ab + {b^2}}}{{{a^2} - {b^2}}} + \\frac{{{a^2} - 4{b^2}}}{{{a^2} - {b^2}}} - \\frac{{{a^2} - 4ab + 3{b^2}}}{{{a^2} - {b^2}}}\\\\ = \\frac{{{a^2} + 6ab - 6{b^2}}}{{{a^2} - {b^2}}}\\end{array}\\)</p>\r\n<p>d)</p>\r\n<p>\\(\\begin{array}{l}\\frac{x}{{{x^2} + xy}} - \\frac{y}{{{x^2} - {y^2}}} + \\frac{{x + y}}{{xy - {y^2}}} = \\frac{x}{{x\\left( {x + y} \\right)}} - \\frac{y}{{\\left( {x + y} \\right)\\left( {x - y} \\right)}} + \\frac{{x + y}}{{y\\left( {x - y} \\right)}}\\\\ = \\frac{{xy\\left( {x - y} \\right)}}{{xy\\left( {{x^2} - {y^2}} \\right)}} - \\frac{{x{y^2}}}{{xy\\left( {{x^2} - {y^2}} \\right)}} + \\frac{{x{{\\left( {x + y} \\right)}^2}}}{{xy\\left( {{x^2} - {y^2}} \\right)}}\\\\ = \\frac{{{x^2}y - x{y^2} - x{y^2} + {x^3} + 2{x^2}y + x{y^2}}}{{xy\\left( {{x^2} - {y^2}} \\right)}}\\\\ = \\frac{{{x^3} + {x^2}y - x{y^2}}}{{xy\\left( {{x^2} - {y^2}} \\right)}} = \\frac{{{x^2} + xy - {y^2}}}{{y\\left( {{x^2} - {y^2}} \\right)}}\\end{array}\\)</p>","common_article":"","display_type":1,"vungoi_exam_id":"","article_type":1,"cmt_count":0,"zip_status":1,"last_modified_time":1686388244,"last_zip_time":1686388244,"zip_link":"https://offline.loigiaihay.com/articles/1439/141106/141106_1686388244.zip","picture":"https://img.loigiaihay.com/picture/article/2023/0610/1-0_69.png","youtube_id":"","video_start_time":"0","quizlet_id":"0","ref_article_id":0,"readmore_display_type":0,"wiki":0,"comment_url":"https://loigiaihay.com/comment/giai-bai-215-trang-46-sgk-toan-8-cung-kham-pha-c1439a141106.html","origin_url":"https://loigiaihay.com/giai-bai-215-trang-46-sgk-toan-8-cung-kham-pha-c1439a141106.html","relate_link":[],"exam_file":"","solution_file":""},"callouts":[],"relate_articles":[],"others_in_cat":[{"article_id":141107,"cat_id":1439,"publish_time":1686388200,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2023/0610/resize_1-0_70.png","title":"Giải bài 2.16 trang 46 SGK Toán 8 - 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