{"id":72,"date":"2023-06-21T13:22:30","date_gmt":"2023-06-21T13:22:30","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-rational-expressions\/"},"modified":"2023-06-21T13:22:30","modified_gmt":"2023-06-21T13:22:30","slug":"summary-rational-expressions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-rational-expressions\/","title":{"raw":"Summary: Rational Expressions","rendered":"Summary: Rational Expressions"},"content":{"raw":"\n\n<h2>Key Concepts<\/h2>\n<ul>\n \t<li>Rational expressions can be simplified by canceling common factors in the numerator and denominator.<\/li>\n \t<li>We can multiply rational expressions by multiplying the numerators and multiplying the denominators.<\/li>\n \t<li>To divide rational expressions, multiply by the reciprocal of the second expression.<\/li>\n \t<li>Adding or subtracting rational expressions requires finding a common denominator.<\/li>\n \t<li>Complex rational expressions have fractions in the numerator or the denominator. These expressions can be simplified.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt><strong>least common denominator<\/strong><\/dt>\n \t<dd id=\"fs-id1165133085665\">the smallest multiple that two denominators have in common<\/dd>\n<\/dl>\n<\/dt>\n<\/dl>\n<\/dt>\n \t<dt>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong>rational expression<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">the quotient of two polynomial expressions<\/dd>\n<\/dl>\n<\/dt>\n<\/dl>\n<\/dt>\n<\/dl>\n\n","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>Rational expressions can be simplified by canceling common factors in the numerator and denominator.<\/li>\n<li>We can multiply rational expressions by multiplying the numerators and multiplying the denominators.<\/li>\n<li>To divide rational expressions, multiply by the reciprocal of the second expression.<\/li>\n<li>Adding or subtracting rational expressions requires finding a common denominator.<\/li>\n<li>Complex rational expressions have fractions in the numerator or the denominator. These expressions can be simplified.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n<dt>\n<\/dt>\n<dt>\n<\/dt>\n<dt><strong>least common denominator<\/strong><\/dt>\n<dd id=\"fs-id1165133085665\">the smallest multiple that two denominators have in common<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n<dt>\n<\/dt>\n<dt><strong>rational expression<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">the quotient of two polynomial expressions<\/dd>\n<\/dl>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-72\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: OpenStax College Algebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":395986,"menu_order":18,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College Algebra\",\"author\":\"OpenStax College 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