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Tasks include working with unlike denominators, combining terms, and reducing expressions to factored or simplified forms. The sheet contains a large set of numbered problems and sections prompting critical thinking, such as splitting expressions into sums of rational expressions. Answers are designed to build procedural accuracy and algebraic simplification skills.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/addingsubtracting-rational-expressions-simplify-each-expression-worksheets/522580/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/addingsubtracting-rational-expressions-simplify-each-expression-worksheets/522580.png","ImageObject",300,407,{"name":92,"@type":93},"Miles","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the main skill this worksheet practices?","Question",{"text":113,"@type":114},"It practices adding and subtracting rational expressions, focusing on simplifying each expression to an equivalent simplest form.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do the critical thinking problems differ from the numbered practice problems?",{"text":118,"@type":114},"Critical thinking questions emphasize strategy, such as splitting a rational expression into a sum with unlike denominators, rather than only direct simplification.",{"name":120,"@type":111,"acceptedAnswer":121},"What should you do when problems have unlike denominators?",{"text":122,"@type":114},"Rewrite the expressions with a common denominator (or an appropriate decomposition) so like terms can be combined and the result can be simplified.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},522580,1791493080,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":52,"preview_page_count":4},13056703019404,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Kuta Software-Infinite Algebra 2 Name   \nAdding/Subtracting Rational Expressions Date  Period   \nSimplify each expression.  \n1) u~~ ~~−8vv + ~~ ~~6u−8v3v~~ ~~ 2) m~~ ~~−6m33nn − m~~ ~~+6m33nn  \n3)  5  +  5a + 1  4)  5  +  n − 6  a 2 + 3a + 2 a 2 + 3a + 2 10n2 + 16n + 6 10n2 + 16n + 6  \n5)  r + 6  +  r + 1  6)  x + 2  −  x + 3   \n3r − 6 3r − 6 2x2 + 13x + 20 2x2 + 13x + 20  \n7)  6  − 5x  8) 6 −  x + 5  x − 1 4 (7x − 5)(x + 4)  \n9)  3  +  4  10)  3  − 7 x + 7 x − 8 4v2 + 4v 2  \n11) 73 − ~~ ~~12x8−~~ ~~8~~ ~~ 12) n~~ ~~~~ ~~5 + ~~ ~~2n4~~ ~~6  \n13) 5x2~~ ~~4 + ~~ ~~2x6~~ ~~3~~ ~~ 14) 3x2~~ ~~~~ ~~12x~~ ~~ + ~~ ~~82x  \n15) n1 + ~~ ~~n~~ ~~~~ ~~7~~ ~~ 16) n~~ ~~~~ ~~8 + ~~ ~~n~~ ~~~~ ~~1  \n17) 38 − 3x~~ ~~4~~ ~~ 18) b~~ ~~~~ ~~8 + ~~ ~~b~~ ~~~~ ~~3  \n19) x~~ ~~~~ ~~6 + ~~ ~~x~~ ~~~~ ~~2~~ ~~ 20) x~~ ~~~~ ~~1 − x~~ ~~~~ ~~2  \n21) 5n2~~ ~~n3+5n5−~~ ~~40 + ~~ ~~7n3n~~ ~~ 22) n~~ ~~~~ ~~5 + ~~ ~~3n~~ ~~8  \n254~~ ~~ 24) 4~~ ~~8~~ ~~16~~ ~~  \n23) ~~ ~~ ~~ ~~ + ~~ ~~  \n1  4  9 9  \n−  \n5 25  \na  a   5  \n−  \n25) 25 5  26)  4   \na 5  4  \n−  \nm m  \nCritical thinking questions:  \na c 28) Split into a sum of two rational expressions  \n27) Simplify:  b + d  with unlike denominators:  \n2x + 3  \nx 2 + 3x + 2  \nKuta Software-Infinite Algebra 2 Name   \nAdding/Subtracting Rational Expressions Date  Period   \nSimplify each expression.  \n1)  \nu − v  \n8v  \n+  \n6u − 3v 8v  \n7u − 4v  \n8v  \n3) a~~ ~~2~~ ~~+~~ ~~53a~~ ~~+~~ ~~2 + ~~ ~~a~~ ~~2~~ ~~+3a~~ ~~~~ ~~2  \n6 + 5a  \na 2 + 3a + 2  \nr + 6 r + 1 5) ~~ ~~ + ~~ ~~  \n3r − 6 3r − 6  \n2r + 7  \n3r − 6  \n6 5x  \n7) ~~ ~~ − ~~  ~~x − 1 4  \n24 − 5x2 + 5x  \n4(x − 1)  \n3 4  \n9) ~~ ~~ + ~~  ~~x + 7 x − 8  \n 7x + 4 (x + 7)(x − 8)  \n11) 73 − ~~ ~~12x8−~~ ~~8  \n21x − 20 3(3x − 2)  \n2x 6x  \n13) ~~ ~~ + ~~ ~~  \n5x + 4 2x + 3  \n34x2 + 30x  \n(5x + 4)(2x + 3)  \nm − 3n m + 3n  \n2) ~~ ~~ − ~~ ~~  \n6m3 n 6m3 n  \n 1   \n−  \nm 3  \n5 n − 6  \n4) ~~ ~~ + ~~ ~~  \n10n2 + 16n + 6 10n2 + 16n + 6  \n−1 + n  \n10n2 + 16n + 6  \nx + 2 x + 3  \n6) ~~ ~~ − ~~ ~~  \n2x2 + 13x + 20 2x2 + 13x + 20  \n 1   \n−  \n2x2 + 13x + 20  \n8) 6 −  x + 5 (7x − 5)(x + 4)  \n42x2 + 137x − 125 (7x − 5)(x + 4)  \n3 7  \n10) ~~ ~~ − ~~ ~~  \n4v2 + 4v 2  \n3 − 14v2 − 14v  \n4v(v + 1)  \n12) n~~ ~~~~ ~~5 + ~~ ~~2n4~~ ~~6  \n15n + 15 + 2n2   \n(n + 3)(n + 5)  \n2 8  \n14) ~~ ~~ + ~~ ~~  \n3x2 + 12x 2x  \n50 + 12x   \n3x(x + 4)  \n15) n1 + ~~ ~~n~~ ~~~~ ~~7  \n7n2 − 41n + 8 (n + 1)(n − 7)  \n17) 38 − 3x~~ ~~4  \n9x − 12  \n8(3x + 4)  \n19) x~~ ~~~~ ~~6 + ~~ ~~x~~ ~~~~ ~~2  \n 10x + 36   \n(x + 6)(x − 2)  \n5n + 5 7n 21) ~~ ~~ + ~~ ~~  \n5n2 + 35n − 40 3n  \n52n − 53 + 7n2  \n23)  \n25)  \n3(n + 8)(n − 1) 25  \n4  \n\n| 1  4 \u003Cbr>−\u003Cbr>5 25\u003Cbr>625\u003Cbr>4\u003Cbr>a  a |\n| --- |\n| 25 − 5 |\n\na  \n 4   \n−  \n25  \nCritical thinking questions:  \n27) Simplify: ~~ ~~ab + cd  \nad + bc  \nbd  \n16)  \n18)  \n20)  \n22)  \n24)  \n26)  \n 2  +  4  n + 8 n + 1  \n6n + 34  \n\n| (n + 1)(n + 8)\u003Cbr> 3  +  7  b − 8 b + 3\u003Cbr>10b − 47 |\n| --- |\n| (b + 3)(b − 8)\u003Cbr>4 2 |\n| −\u003Cbr>x + 1 x + 2\u003Cbr>2x + 6 |\n\n(x + 1)(x + 2)  \n 3  +  6  n − 5 3n − 8  \n15n − 54  \n(3n − 8)(n − 5)  \n8  \n49 + ~~ ~~169  \n18  \n5  \n5  \n4  \n5  4  \n−  \nm m  \n5m  \n4  \n28) Split into a sum of two rational expressions with unlike denominators:  \n2x + 3  \nx 2 + 3x + 2  \nMany solutions. Ex: x~~ ~~~~ ~~1 + ~~ ~~x~~ ~~~~ ~~2  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaidWkE9el7phW","https://ap.wps.com/l/cbCaidWkE9el7phW","pdf",39981,"English","# Simplify each expression\n## Adding and subtracting rational expressions\n## Critical thinking questions","[{\"question\":\"What is the main skill this worksheet practices?\",\"answer\":\"It practices adding and subtracting rational expressions, focusing on simplifying each expression to an equivalent simplest form.\"},{\"question\":\"How do the critical thinking problems differ from the numbered practice problems?\",\"answer\":\"Critical thinking questions emphasize strategy, such as splitting a rational expression into a sum with unlike denominators, rather than only direct simplification.\"},{\"question\":\"What should you do when problems have unlike denominators?\",\"answer\":\"Rewrite the expressions with a common denominator (or an appropriate decomposition) so like terms can be combined and the result can be simplified.\"}]","Adding/Subtracting Rational Expressions - Simplify Each Expression - Worksheets | PDF",1791425938]