{"id":717,"date":"2025-06-20T17:07:17","date_gmt":"2025-06-20T17:07:17","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/?post_type=chapter&#038;p=717"},"modified":"2025-10-08T04:12:16","modified_gmt":"2025-10-08T04:12:16","slug":"partial-fractions-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/partial-fractions-apply-it\/","title":{"raw":"Partial Fractions: Apply It","rendered":"Partial Fractions: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Break down and integrate rational functions using partial fractions<\/li>\r\n \t<li>Identify and work with simple linear factors in rational functions<\/li>\r\n \t<li>Handle repeated linear factors when using partial fractions<\/li>\r\n \t<li>Work with quadratic factors in rational functions<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Breaking Down Complex Problems: Real-World Applications of Partial Fractions<\/h2>\r\nEngineers, scientists, and economists often work with formulas that involve fractions of polynomials. For example, in electrical engineering, circuit behavior can be modeled by rational functions where breaking them into partial fractions makes integration possible. Let\u2019s practice decomposing rational functions and integrating them so we can better understand how these mathematical tools apply to real problems.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p data-start=\"1576\" data-end=\"1953\">[ohm_question hide_question_numbers=1]313325[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p data-start=\"1977\" data-end=\"2026\">[ohm_question hide_question_numbers=1]313366[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p data-start=\"3029\" data-end=\"3088\">[ohm_question hide_question_numbers=1]313367[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Break down and integrate rational functions using partial fractions<\/li>\n<li>Identify and work with simple linear factors in rational functions<\/li>\n<li>Handle repeated linear factors when using partial fractions<\/li>\n<li>Work with quadratic factors in rational functions<\/li>\n<\/ul>\n<\/section>\n<h2>Breaking Down Complex Problems: Real-World Applications of Partial Fractions<\/h2>\n<p>Engineers, scientists, and economists often work with formulas that involve fractions of polynomials. For example, in electrical engineering, circuit behavior can be modeled by rational functions where breaking them into partial fractions makes integration possible. Let\u2019s practice decomposing rational functions and integrating them so we can better understand how these mathematical tools apply to real problems.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p data-start=\"1576\" data-end=\"1953\"><iframe loading=\"lazy\" id=\"ohm313325\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313325&theme=lumen&iframe_resize_id=ohm313325&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p data-start=\"1977\" data-end=\"2026\"><iframe loading=\"lazy\" id=\"ohm313366\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313366&theme=lumen&iframe_resize_id=ohm313366&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p data-start=\"3029\" data-end=\"3088\"><iframe loading=\"lazy\" id=\"ohm313367\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313367&theme=lumen&iframe_resize_id=ohm313367&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":24,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":541,"module-header":"- Select Header -","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\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/717"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":10,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/717\/revisions"}],"predecessor-version":[{"id":2403,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/717\/revisions\/2403"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/541"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/717\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=717"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=717"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=717"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}