{"id":1261,"date":"2016-10-21T21:20:01","date_gmt":"2016-10-21T21:20:01","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&#038;p=1261"},"modified":"2017-08-15T20:52:38","modified_gmt":"2017-08-15T20:52:38","slug":"introductionrational-expressions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/introductionrational-expressions\/","title":{"raw":"Introduction to Rational Expressions","rendered":"Introduction to Rational Expressions"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Simplify rational expressions.<\/li>\r\n \t<li>Multiply rational expressions.<\/li>\r\n \t<li>Divide rational expressions.<\/li>\r\n \t<li>Add and subtract rational expressions.<\/li>\r\n \t<li>Simplify complex rational expressions.<\/li>\r\n<\/ul>\r\n<\/div>\r\nA pastry shop has fixed costs of [latex]\\$280[\/latex] per week and variable costs of [latex]\\$9[\/latex] per box of pastries. The shop\u2019s costs per week in terms of [latex]x[\/latex], the number of boxes made, is [latex]280+9x[\/latex]. We can divide the costs per week by the number of boxes made to determine the cost per box of pastries.\r\n<p style=\"text-align: center;\">[latex]\\frac{280+9x}{x}[\/latex]<\/p>\r\nNotice that the result is a polynomial expression divided by a second polynomial expression. In this section, we will explore quotients of polynomial expressions.","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Simplify rational expressions.<\/li>\n<li>Multiply rational expressions.<\/li>\n<li>Divide rational expressions.<\/li>\n<li>Add and subtract rational expressions.<\/li>\n<li>Simplify complex rational expressions.<\/li>\n<\/ul>\n<\/div>\n<p>A pastry shop has fixed costs of [latex]\\$280[\/latex] per week and variable costs of [latex]\\$9[\/latex] per box of pastries. The shop\u2019s costs per week in terms of [latex]x[\/latex], the number of boxes made, is [latex]280+9x[\/latex]. We can divide the costs per week by the number of boxes made to determine the cost per box of pastries.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{280+9x}{x}[\/latex]<\/p>\n<p>Notice that the result is a polynomial expression divided by a second polynomial expression. In this section, we will explore quotients of polynomial expressions.<\/p>\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-1261\">\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":21,"menu_order":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College Algebra\",\"author\":\"OpenStax College Algebra\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et 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