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Students are instructed to simplify each given expression through factorization and multiplication of rational terms, including products of algebraic factors and binomials. Problems include expressions with variables in numerators and denominators such as n, r, p, v, x, a, b, and m, often requiring cancellation of common factors. Each item follows a “Simplify each expression” directive for step-by-step algebraic simplification.","Kuta Software-Infinite Algebra 1 Name___________________________________  \nMultiplying Rational Expressions Date________________ Period____  \nSimplify each expression.  \n1) 59n99 ⋅ ~~ ~~8033n~~ ~~ 2) 5343 ⋅ ~~ ~~46n312  \n 93   34n   79n   85   \n3) ⋅ 4) ⋅ 2  \n21n 51n 25 27n  \n 96   25   84   48x  \n5) ⋅ 6) ⋅  \n38n 45 3 95  \n6(r + 2) 4r 7n2 (n + 4) n − 3  \n7) ~~ ~~ ⋅ ~~ ~~ 8) ~~ ~~ ⋅  \n20 6(r + 2) (n − 3)(n + 4) (n + 8)(n + 6)  \n2( p + 6)   p − 3   9(r + 4)   9r   \n9) ⋅ 10) ⋅  \n4 2( p − 3) r + 4 9(r − 5)  \n8(m + 1)   9   ( p + 6)( p − 4)   1   \n11) ⋅ 12) ⋅  \n7m 8(m + 1) p − 4 ( p − 4)( p − 2)  \n 1   10v + 30   7n   9n − 24  \n13) ⋅ 14) ⋅  \nv + 10 v + 3 24n3 − 64n2 7n  \n15) 7xx~~ ~~~~ ~~735 ⋅ ~~ ~~x2~~ ~~−x~~ ~~40~~ ~~ 16) 20a2a~~ ~~−~~ ~~1100a ⋅ ~~ ~~16a3~~ ~~~~ ~~80a2~~ ~~  \n17) 3b2b~~ ~~~~ ~~186b ⋅ ~~ ~~b~~ ~~~~ ~~8~~ ~~ 18) pp710 ⋅ ~~ ~~7pp~~ ~~~~ ~~214  \n21x2 − 21x 6x 1 p 2 + 6 p − 27 19) ~~ ~~ ⋅ ~~ ~~ 20) ~~ ~~ ⋅ ~~ ~~  \n18x2 − 18x 6x2 p − 9 p + 9  \nv − 7   10v + 60   5r + 50   r − 2  \n21) ⋅ 22) ⋅  \nv + 6 v − 7 r + 10 5  \n23) x~~ ~~21−01xx1+0250~~ ~~ ⋅ x45109x~~ ~~ 24) 4x29 ⋅ ~~ ~~x23x−3~~ ~~x1−~~ ~~32x26~~ ~~  \n25) 8v8v~~ ~~~~ ~~5648 ⋅ ~~ ~~v~~ ~~28+v2+~~ ~~1824v~~ ~~ 26) 9r39r2~~ ~~54r245r~~ ~~ ⋅ ~~ ~~99rr3+59r4r2~~ ~~  \n27) 3mm~~ ~~~~ ~~115 ⋅ m~~ ~~29−m10~~ ~~ 28) 6nn96 ⋅ n~~ ~~2~~ ~~+66n~~ ~~−6~~ ~~27  \nKuta Software-Infinite Algebra 1 Name   \nMultiplying Rational Expressions Date  Period   \nSimplify each expression.  \n1) 59n99 ⋅ ~~ ~~8033n  \n47203267  \n3) 9321n ⋅ ~~ ~~3541nn  62  21n  \n5) 9638n ⋅ ~~ ~~2455  80  57n  \n6(r + 2) 4r  \n7) ~~ ~~ ⋅ ~~ ~~  \n20 6(r + 2)  \n r  \n5  \n2( p + 6) p − 3  \n9) ~~ ~~ ⋅  \n4 2( p − 3)  \np + 6  \n4  \n8(m + 1) 9 11) ~~ ~~ ⋅ ~~ ~~  \n7m 8(m + 1)  \n 9   \n7m  \n 1   10v + 30  \n13) ⋅  \nv + 10 v + 3  \n 10   \nv + 10  \n2)  \n53 46n2  \n43 31  \n2438n2  \n1333  \n4) 79n 85   \n25 27n2 1343  \n135n  \n84   48x 6) ⋅  \n3 95  \n1344x  \n95  \n7n2 (n + 4) n − 3  \n8) ~~ ~~ ⋅  \n(n − 3)(n + 4) (n + 8)(n + 6)  \n 7n2   \n(n + 8)(n + 6)  \n9(r + 4)   9r   \n10) ⋅ r + 4 9(r − 5)  \n 9r r − 5  \n( p + 6)( p − 4) 1  \n12) ~~ ~~ ⋅  \np − 4 ( p − 4)( p − 2)  \n p + 6   \n( p − 4)( p − 2)  \n 7n   9n − 24  \n14) ⋅  \n24n3 − 64n2 7n  \n 3   \n8n2  \n15)  \n17)  \n19)  \n21)  \n23)  \n25)  \n27)  \nx + 7 x2 − 3x − 40  \n7x + 35 x − 8 x + 7  \n7  \n3b2 + 18b 1  b + 6 b + 8  \n3b  \nb + 8  \n21x2 − 21x 6x  \n18x2 − 18x 6x2  7   \n6x  \nv − 7 10v + 60  \nv + 6 v − 7  \n10  \nx 2 − 10x + 25 x − 10  \n10x − 100 45 − 9x  \n(x − 5)  \n−  \n90  \n8v − 56 v 2 + 9v + 18  \n8v + 48 8v2 + 24v v − 7  \n8v  \nm + 1 8m − 80  \n3m − 15 m 2 − 9m − 10 8  \n3(m − 5)  \n16) 20a2a~~ ~~−~~ ~~1100a ⋅ ~~ ~~16a3~~ ~~~~ ~~80a2~~  ~~5  \n4a(a − 1)  \np + 7 p + 2 18) ~~ ~~ ⋅ ~~ ~~  \np − 10 7 p + 14  \np + 7  \n7( p − 10)  \n20)  \n22)  \n24)  \n 1 p 2 + 6 p − 27 p − 9 p + 9  \np − 3  \np − 9  \n5r + 50   r − 2 ⋅  \nr + 10 5  \nr − 2  \n45x2 x2 − 5x − 36  x − 9 3x3 + 12x2  \n15  \n26) 9r39r2~~ ~~54r245r~~ ~~ ⋅ ~~ ~~99rr3+59r4r2~~ ~~  \nr + 1  \nr + 5  \n28)  \n6n + 6 n 2 + 6n − 27  \nn + 9 6n + 6 n − 3  \nCreate your own worksheets like this one with Infinite Algebra 1. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaie32DMljJtJi","https://ap.wps.com/l/cbCaie32DMljJtJi","pdf",38105,11,"English","en",105,"# Simplify each expression\n## Multiplying rational expressions","[{\"question\":\"What is the main task on this worksheet?\",\"answer\":\"Simplify each multiplying rational expression shown in the problems.\"},{\"question\":\"How should students approach the expressions?\",\"answer\":\"Multiply and combine rational terms by factoring and then canceling common factors when possible.\"},{\"question\":\"Do the problems use different variables and formats?\",\"answer\":\"Yes. The worksheet includes expressions using variables like n, r, p, v, x, a, b, and m, with various factored binomials in numerators and denominators.\"}]","Multiplying Rational Expressions - Simplify Each Expression | PDF",1791425859,{"code":4,"msg":81,"data":82},"ok",{"site_id":75,"language":74,"slug":83,"title":65,"keywords":84,"description":66,"schema_data":85,"social_meta":139,"head_meta":141,"extra_data":143,"updated_unix":144},"multiplying-rational-expressions-simplify-each-expression","",{"@graph":86,"@context":138},[87,101,121],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,99],{"item":91,"name":92,"@type":93,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":9,"@type":93,"position":14},"https://docshare.wps.com/document/",{"item":97,"name":20,"@type":93,"position":98},"https://docshare.wps.com/document/exam/",3,{"item":100,"name":65,"@type":93,"position":19},"https://docshare.wps.com/document/multiplying-rational-expressions-simplify-each-expression/522510/",{"url":100,"name":65,"@type":102,"image":103,"author":108,"headline":65,"publisher":110,"fileFormat":113,"inLanguage":74,"description":66,"dateModified":114,"datePublished":115,"encodingFormat":113,"isAccessibleForFree":116,"interactionStatistic":117},"DigitalDocument",{"url":104,"@type":105,"width":106,"height":107},"https://docshare.wps.com/thumbnails/multiplying-rational-expressions-simplify-each-expression/522510.png","ImageObject",300,407,{"name":63,"@type":109},"Person",{"url":91,"name":111,"@type":112},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":118,"interactionType":119,"userInteractionCount":72},"InteractionCounter",{"@type":120},"ViewAction",{"@type":122,"mainEntity":123},"FAQPage",[124,130,134],{"name":125,"@type":126,"acceptedAnswer":127},"What is the main task on this worksheet?","Question",{"text":128,"@type":129},"Simplify each multiplying rational expression shown in the problems.","Answer",{"name":131,"@type":126,"acceptedAnswer":132},"How should students approach the expressions?",{"text":133,"@type":129},"Multiply and combine rational terms by factoring and then canceling common factors when possible.",{"name":135,"@type":126,"acceptedAnswer":136},"Do the problems use different variables and formats?",{"text":137,"@type":129},"Yes. The worksheet includes expressions using variables like n, r, p, v, x, a, b, and m, with various factored binomials in numerators and denominators.","https://schema.org",{"og:url":100,"og:type":140,"og:title":65,"og:site_name":111,"og:description":66},"article",{"robots":142,"canonical":100},"index,follow",{"doc_id":61,"site_id":75},1791511562]