{"id":887,"date":"2024-04-30T19:39:17","date_gmt":"2024-04-30T19:39:17","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=887"},"modified":"2024-11-20T02:44:00","modified_gmt":"2024-11-20T02:44:00","slug":"rational-expressions-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/rational-expressions-learn-it-1\/","title":{"raw":"Rational Expressions: Learn It 1","rendered":"Rational Expressions: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Simplify rational expressions<\/li>\r\n \t<li>Practice how to multiply, divide, add, and subtract rational expressions<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Rational Expressions<\/h2>\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]\\Large{\\dfrac{280+9x}{x}}[\/latex]<\/p>\r\nNotice that the result is a polynomial expression divided by a second polynomial expression. This is known as a rational expression.\r\n\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>rational expressions<\/h3>\r\n<strong>Rational expressions<\/strong> are formed when one polynomial is divided by another, resulting in a fraction-like form where the numerator and the denominator are both polynomials.\r\n<p style=\"text-align: center;\">[latex]\\dfrac{P(x)}{Q(x)}[\/latex] where [latex]P(x)[\/latex] and [latex]Q(x)[\/latex] are polynomials.<\/p>\r\n\r\n<\/section>\r\n<p class=\"whitespace-pre-wrap break-words\">The domain of a rational expression includes all real numbers except those that make the denominator equal to zero. When the denominator equals zero, the expression is undefined. This concept is rooted in the fundamental principle that division by zero is impossible in mathematics.<\/p>\r\n\r\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<h3>rational expressions and undefined values<\/h3>\r\nA rational expression is undefined when its denominator equals zero.\r\n\r\n<\/section><section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How to: Find the undefined values of a rational expression<\/strong>\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Isolate the denominator.<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Set the denominator equal to zero.<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Solve the resulting equation.<\/li>\r\n<\/ol>\r\n<p class=\"whitespace-pre-wrap break-words\">The solutions to this equation are the values that make the rational expression undefined.<\/p>\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p class=\"whitespace-pre-wrap break-words\">Determine the value(s) of [latex]x[\/latex] for which the following rational expression is undefined:<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\" style=\"text-align: center;\">[latex]\\frac{x^2 - 4}{x - 2}[\/latex]<\/p>\r\n[reveal-answer q=\"138302\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"138302\"]\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Identify the denominator: [latex](x - 2)[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Set the denominator to zero: [latex]x - 2 = 0[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Solve for [latex]x[\/latex]:\r\n[latex]x = 2[\/latex]<\/li>\r\n<\/ol>\r\n<p class=\"whitespace-pre-wrap break-words\">Therefore, the expression is undefined when [latex]x = 2[\/latex].<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">Note: At [latex]x = 2[\/latex], both the numerator and denominator equal zero, creating an [pb_glossary id=\"4395\"]indeterminate form[\/pb_glossary] [latex]\\frac{0}{0}[\/latex].<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p class=\"whitespace-pre-wrap break-words\">Find the values of [latex]x[\/latex] that make the following rational expression undefined:<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\" style=\"text-align: center;\">[latex]\\frac{x^2 + 3x}{x^2 - 4}[\/latex]<\/p>\r\n[reveal-answer q=\"298475\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"298475\"]\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Identify the denominator: [latex](x^2 - 4)[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Set the denominator to zero: [latex]x^2 - 4 = 0[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Factor the equation: [latex](x + 2)(x - 2) = 0[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Solve for [latex]x[\/latex]:\r\n[latex]x + 2 = 0[\/latex] or [latex]x - 2 = 0[\/latex]\r\n[latex]x = -2[\/latex] or [latex]x = 2[\/latex]<\/li>\r\n<\/ol>\r\n<p class=\"whitespace-pre-wrap break-words\">Therefore, the expression is undefined when [latex]x = 2[\/latex] or [latex]x = -2[\/latex].<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p class=\"whitespace-pre-wrap break-words\">Determine all values of [latex]x[\/latex] for which the following rational expression is undefined:<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\" style=\"text-align: center;\">[latex]\\frac{2x^2 - 5}{x^3 - x}[\/latex]<\/p>\r\n[reveal-answer q=\"156506\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"156506\"]\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Identify the denominator: [latex]x^3 - x[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Factor the denominator: [latex]x(x^2 - 1) = x(x + 1)(x - 1)[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Set each factor to zero and solve:\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">\u00a0[latex]x = 0[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">[latex]x + 1 = 0[\/latex], so [latex]x = -1[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">[latex]x - 1 = 0[\/latex], so [latex]x = 1[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<p class=\"whitespace-pre-wrap break-words\">Therefore, the expression is undefined when [latex]x = 0[\/latex], [latex]x = 1[\/latex], and [latex]x = -1[\/latex].<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section>We can apply the properties of fractions to rational expressions such as simplifying the expressions by canceling common factors from the numerator and the denominator. To do this, we first need to factor both the numerator and denominator. Let\u2019s start with the rational expression shown.\r\n<p style=\"text-align: center;\">[latex]\\dfrac{{x}^{2}+8x+16}{{x}^{2}+11x+28}[\/latex]<\/p>\r\nWe can factor the numerator and denominator to rewrite the expression as [latex]\\dfrac{{\\left(x+4\\right)}^{2}}{\\left(x+4\\right)\\left(x+7\\right)}[\/latex].\r\n<div>Then we can simplify the expression by canceling the common factor [latex]\\left(x+4\\right)[\/latex] to get [latex]\\dfrac{x+4}{x+7}[\/latex].<\/div>\r\n<div><\/div>\r\n<div><section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How To: Given a rational expression, simplify it<\/strong>\r\n<ol>\r\n \t<li>Factor the numerator and denominator.<\/li>\r\n \t<li>Cancel any common factors.<\/li>\r\n<\/ol>\r\n<\/section><\/div>\r\n<section class=\"textbox example\">Simplify [latex]\\dfrac{{x}^{2}-9}{{x}^{2}+4x+3}[\/latex].[reveal-answer q=\"568949\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"568949\"][latex]\\begin{array}{lllllllll}\\dfrac{\\left(x+3\\right)\\left(x - 3\\right)}{\\left(x+3\\right)\\left(x+1\\right)}\\hfill &amp; \\hfill &amp; \\hfill &amp; \\hfill &amp; \\text{Factor the numerator and the denominator}.\\hfill \\\\ \\dfrac{x - 3}{x+1}\\hfill &amp; \\hfill &amp; \\hfill &amp; \\hfill &amp; \\text{Cancel common factor }\\left(x+3\\right).\\hfill \\end{array}[\/latex]<strong>Analysis of the Solution<\/strong>We can cancel the common factor because any expression divided by itself is equal to 1.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>Can the [latex]{x}^{2}[\/latex] term be cancelled in the above example?<\/strong><em>No. A factor is an expression that is multiplied by another expression. The term [latex]x^2[\/latex] is part of the polynomial terms in both the numerator and denominator, but it is not a standalone factor.<\/em><em>Polynomial expressions need to be fully factored, and only common binomial or monomial factors that appear as a product in both the numerator and denominator can be canceled. Canceling should only occur with factors, not terms that are part of a sum or difference in the polynomials, as altering these without proper factoring could change the value of the expression.<\/em><\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18897[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18898[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Simplify rational expressions<\/li>\n<li>Practice how to multiply, divide, add, and subtract rational expressions<\/li>\n<\/ul>\n<\/section>\n<h2>Rational Expressions<\/h2>\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]\\Large{\\dfrac{280+9x}{x}}[\/latex]<\/p>\n<p>Notice that the result is a polynomial expression divided by a second polynomial expression. This is known as a rational expression.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>rational expressions<\/h3>\n<p><strong>Rational expressions<\/strong> are formed when one polynomial is divided by another, resulting in a fraction-like form where the numerator and the denominator are both polynomials.<\/p>\n<p style=\"text-align: center;\">[latex]\\dfrac{P(x)}{Q(x)}[\/latex] where [latex]P(x)[\/latex] and [latex]Q(x)[\/latex] are polynomials.<\/p>\n<\/section>\n<p class=\"whitespace-pre-wrap break-words\">The domain of a rational expression includes all real numbers except those that make the denominator equal to zero. When the denominator equals zero, the expression is undefined. This concept is rooted in the fundamental principle that division by zero is impossible in mathematics.<\/p>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<h3>rational expressions and undefined values<\/h3>\n<p>A rational expression is undefined when its denominator equals zero.<\/p>\n<\/section>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How to: Find the undefined values of a rational expression<\/strong><\/p>\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Isolate the denominator.<\/li>\n<li class=\"whitespace-normal break-words\">Set the denominator equal to zero.<\/li>\n<li class=\"whitespace-normal break-words\">Solve the resulting equation.<\/li>\n<\/ol>\n<p class=\"whitespace-pre-wrap break-words\">The solutions to this equation are the values that make the rational expression undefined.<\/p>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p class=\"whitespace-pre-wrap break-words\">Determine the value(s) of [latex]x[\/latex] for which the following rational expression is undefined:<\/p>\n<p class=\"whitespace-pre-wrap break-words\" style=\"text-align: center;\">[latex]\\frac{x^2 - 4}{x - 2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q138302\">Show Answer<\/button><\/p>\n<div id=\"q138302\" class=\"hidden-answer\" style=\"display: none\">\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Identify the denominator: [latex](x - 2)[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Set the denominator to zero: [latex]x - 2 = 0[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Solve for [latex]x[\/latex]:<br \/>\n[latex]x = 2[\/latex]<\/li>\n<\/ol>\n<p class=\"whitespace-pre-wrap break-words\">Therefore, the expression is undefined when [latex]x = 2[\/latex].<\/p>\n<p class=\"whitespace-pre-wrap break-words\">Note: At [latex]x = 2[\/latex], both the numerator and denominator equal zero, creating an <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_887_4395\">indeterminate form<\/a> [latex]\\frac{0}{0}[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p class=\"whitespace-pre-wrap break-words\">Find the values of [latex]x[\/latex] that make the following rational expression undefined:<\/p>\n<p class=\"whitespace-pre-wrap break-words\" style=\"text-align: center;\">[latex]\\frac{x^2 + 3x}{x^2 - 4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q298475\">Show Answer<\/button><\/p>\n<div id=\"q298475\" class=\"hidden-answer\" style=\"display: none\">\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Identify the denominator: [latex](x^2 - 4)[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Set the denominator to zero: [latex]x^2 - 4 = 0[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Factor the equation: [latex](x + 2)(x - 2) = 0[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Solve for [latex]x[\/latex]:<br \/>\n[latex]x + 2 = 0[\/latex] or [latex]x - 2 = 0[\/latex]<br \/>\n[latex]x = -2[\/latex] or [latex]x = 2[\/latex]<\/li>\n<\/ol>\n<p class=\"whitespace-pre-wrap break-words\">Therefore, the expression is undefined when [latex]x = 2[\/latex] or [latex]x = -2[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p class=\"whitespace-pre-wrap break-words\">Determine all values of [latex]x[\/latex] for which the following rational expression is undefined:<\/p>\n<p class=\"whitespace-pre-wrap break-words\" style=\"text-align: center;\">[latex]\\frac{2x^2 - 5}{x^3 - x}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q156506\">Show Answer<\/button><\/p>\n<div id=\"q156506\" class=\"hidden-answer\" style=\"display: none\">\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Identify the denominator: [latex]x^3 - x[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Factor the denominator: [latex]x(x^2 - 1) = x(x + 1)(x - 1)[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Set each factor to zero and solve:\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">\u00a0[latex]x = 0[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">[latex]x + 1 = 0[\/latex], so [latex]x = -1[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">[latex]x - 1 = 0[\/latex], so [latex]x = 1[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p class=\"whitespace-pre-wrap break-words\">Therefore, the expression is undefined when [latex]x = 0[\/latex], [latex]x = 1[\/latex], and [latex]x = -1[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/section>\n<p>We can apply the properties of fractions to rational expressions such as simplifying the expressions by canceling common factors from the numerator and the denominator. To do this, we first need to factor both the numerator and denominator. Let\u2019s start with the rational expression shown.<\/p>\n<p style=\"text-align: center;\">[latex]\\dfrac{{x}^{2}+8x+16}{{x}^{2}+11x+28}[\/latex]<\/p>\n<p>We can factor the numerator and denominator to rewrite the expression as [latex]\\dfrac{{\\left(x+4\\right)}^{2}}{\\left(x+4\\right)\\left(x+7\\right)}[\/latex].<\/p>\n<div>Then we can simplify the expression by canceling the common factor [latex]\\left(x+4\\right)[\/latex] to get [latex]\\dfrac{x+4}{x+7}[\/latex].<\/div>\n<div><\/div>\n<div>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How To: Given a rational expression, simplify it<\/strong><\/p>\n<ol>\n<li>Factor the numerator and denominator.<\/li>\n<li>Cancel any common factors.<\/li>\n<\/ol>\n<\/section>\n<\/div>\n<section class=\"textbox example\">Simplify [latex]\\dfrac{{x}^{2}-9}{{x}^{2}+4x+3}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q568949\">Show Solution<\/button><\/p>\n<div id=\"q568949\" class=\"hidden-answer\" style=\"display: none\">[latex]\\begin{array}{lllllllll}\\dfrac{\\left(x+3\\right)\\left(x - 3\\right)}{\\left(x+3\\right)\\left(x+1\\right)}\\hfill & \\hfill & \\hfill & \\hfill & \\text{Factor the numerator and the denominator}.\\hfill \\\\ \\dfrac{x - 3}{x+1}\\hfill & \\hfill & \\hfill & \\hfill & \\text{Cancel common factor }\\left(x+3\\right).\\hfill \\end{array}[\/latex]<strong>Analysis of the Solution<\/strong>We can cancel the common factor because any expression divided by itself is equal to 1.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>Can the [latex]{x}^{2}[\/latex] term be cancelled in the above example?<\/strong><em>No. A factor is an expression that is multiplied by another expression. The term [latex]x^2[\/latex] is part of the polynomial terms in both the numerator and denominator, but it is not a standalone factor.<\/em><em>Polynomial expressions need to be fully factored, and only common binomial or monomial factors that appear as a product in both the numerator and denominator can be canceled. Canceling should only occur with factors, not terms that are part of a sum or difference in the polynomials, as altering these without proper factoring could change the value of the expression.<\/em><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18897\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18897&theme=lumen&iframe_resize_id=ohm18897&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18898\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18898&theme=lumen&iframe_resize_id=ohm18898&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_887_4395\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_887_4395\"><div tabindex=\"-1\"><p>An indeterminate form occurs when a mathematical expression yields an ambiguous result. The form 0\/0 is one such case.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":12,"menu_order":17,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":55,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/887"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":17,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/887\/revisions"}],"predecessor-version":[{"id":6231,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/887\/revisions\/6231"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/55"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/887\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=887"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=887"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=887"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}