[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523490-105":59,"doc-detail-523490-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","rational-equations-solve-each-equation-check-for-extraneous-solutions","Rational Equations - Solve each equation - Check for extraneous solutions","","Rational Equations worksheet from Infinite Precalculus focused on solving rational equations. The problems require students to find solutions to each equation while following the instruction to verify results. Each item is structured as a numbered equation set, emphasizing careful algebraic manipulation and solution checking. The exercise reinforces the need to identify extraneous solutions that can arise when clearing denominators or transforming rational expressions.",{"@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/rational-equations-solve-each-equation-check-for-extraneous-solutions/523490/",{"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/rational-equations-solve-each-equation-check-for-extraneous-solutions/523490.png","ImageObject",300,407,{"name":92,"@type":93},"PakDamar76","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",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the main task of this worksheet?","Question",{"text":113,"@type":114},"Solve each rational equation shown in the numbered problems. Work through the equation and determine the valid solutions.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Why must you check for extraneous solutions?",{"text":118,"@type":114},"Rational equations can generate solutions that do not satisfy the original equation after algebraic steps, especially after clearing denominators. Checking ensures only valid solutions are kept.",{"name":120,"@type":111,"acceptedAnswer":121},"How are the practice problems organized?",{"text":122,"@type":114},"The worksheet lists multiple numbered equations (1 through 16) under the prompt to solve each equation. Each problem follows the same overall requirement to verify solutions.","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},523490,1791518778,{"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},962090893057,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Precalculus Name   \nRational Equations Date  Period   \nSolve each equation. Remember to check for extraneous solutions.  \n1) 􀀗􀀔x 􀀐 􀀔􀀗~~ ~~ 􀀠 􀀔􀀕~~ ~~ 2) 􀀘v~~ ~~􀀐~~ ~~􀀘v 􀀐 􀀘v~~ ~~􀀎v~~ ~~􀀔􀀘~~ ~~ 􀀠 􀀔  \n3) 􀀘a􀀕􀀓 􀀎  􀀠 􀀖􀀕a~~ ~~ 4) ~~􀀕 ~~ 􀀠  􀀎 ~~􀀕 ~~  \n5) 􀀔 􀀎 r~~ ~~~~ ~~􀀕~~ ~~ 􀀠 r~~ ~~~~ ~~􀀕~~ ~~ 6) n~~ ~~􀀔~~ ~~ 􀀠 􀀔 􀀎 􀀕􀀔n  \n7) 􀀘k 􀀠 ~~ ~~􀀔k 􀀐 􀀔 8) 􀀘b 􀀠 􀀔b 􀀎 􀀗  \n9) n~~ ~~~~ ~~􀀔~~ ~~ 􀀐 n~~ 􀀕 ~~􀀎~~ ~~􀀔􀀚n~~ ~~􀀎~~ ~~􀀙~~ ~~ 􀀠 n~~ 􀀕 ~~􀀎~~ ~~􀀖􀀚n~~ ~~􀀎~~ ~~􀀙~~ ~~ 10) r~~ ~~~~ ~~􀀔~~ ~~ 􀀎 􀀗 􀀠 r~~ ~~~~ ~~􀀔~~ ~~  \n11) 􀀖~~ ~~v~~ ~~􀀕~~ ~~~~ ~~~~ ~~~~ ~~ 􀀠 ~~ ~~ 􀀐 v~~ 􀀕 ~~~~ ~~􀀕~~ ~~v~~ ~~ 12) v~~ ~~􀀕v~~ ~~v􀀙􀀎v~~ ~~􀀗~~ ~~ 􀀠 v~~ 􀀕 ~~~~ ~~􀀙v 􀀎 ~~ ~~~~ ~~  \n13) bb~~􀀕 ~~~~ ~~􀀔􀀕b 􀀎 ~~ ~~􀀙~~ ~~b~~ ~~􀀕~~ ~~~~ ~~b􀀕􀀎~~ ~~􀀔􀀛b~~ ~~ 􀀠 􀀕~~ ~~b􀀐~~ ~~􀀗b~~ ~~ 14) b~~ 􀀕 ~~􀀘􀀎~~ ~~b 􀀠 b~~ ~~􀀎b~~ ~~􀀗 􀀎 b~~ 􀀕 ~~~~ ~~b  \n15) n~~ 􀀕 ~~􀀎~~ ~~􀀔~~ ~~􀀔􀀔~~ ~~n~~ ~~􀀎~~ ~~􀀖􀀓~~ ~~ 􀀠 n~~ ~~~~ ~~􀀘 􀀐 􀀗 16) n~~ ~~n􀀎~~ ~~􀀘~~ ~~ 􀀠 􀀕nn~~ ~~􀀎􀀎~~ ~~􀀗􀀔􀀓 􀀎 n􀀕􀀕n􀀎~~􀀕 ~~n􀀔~~ ~~n􀀛~~ ~~  \nKuta Software-Infinite Precalculus Name   \nRational Equations Date  Period   \nSolve each equation. Remember to check for extraneous solutions.  \n1)  \n3)  \n5)  \n7)  \n 􀀔 􀀐  \n􀀗x  \n 􀀔   􀀔   \n􀀠  \n􀀗 􀀕  \n􀁞 ~~ ~~􀀔􀀖~~ ~~􀁠  \n 􀀘a 􀀎 􀀕􀀓 􀀙a  \n􀀎  \n 􀀔   􀀖   \n􀀠  \na 􀀕 a  \n􀁞 􀀐 ~~ ~~􀀔􀀚􀀘~~ ~~ 􀁠  \n􀀔 􀀎 r~~ ~~~~ ~~􀀕~~ ~~ 􀀠 r~~ ~~~~ ~~􀀕~~ ~~  \n􀁞􀀖􀁠  \n~~ ~~􀀘k 􀀠 ~~ ~~􀀔k 􀀐 􀀔  \n􀁞􀀐􀀗􀁠  \n2)  \n4)  \n6)  \n8)  \n􀀘v 􀀐 􀀘 􀀘v 􀀎 􀀔􀀘  \n~~ ~~ 􀀐 ~~ ~~ 􀀠 􀀔  \nv v  \n􀁞􀀐􀀕􀀓􀁠  \n􀀕  \n􀀕  \nm  \n􀀠  \n 􀀔   \nm  \n􀀎  \n􀀔  \n􀀕  \nm  \n􀁞􀀔􀁠  \nn~~ ~~􀀔~~ ~~ 􀀠 􀀔 􀀎 􀀕􀀔n  \n􀁞􀀐􀀕􀁠  \n􀀘b 􀀠 􀀔b 􀀎 􀀗  \n􀁞􀀔􀁠  \n9) n~~ ~~~~ ~~􀀔~~ ~~ 􀀐 n~~ 􀀕 ~~􀀎~~ ~~􀀔􀀚n~~ ~~􀀎~~ ~~􀀙~~ ~~ 􀀠 n~~ 􀀕 ~~􀀎~~ ~~􀀖􀀚n~~ ~~􀀎~~ ~~􀀙~~ ~~ 10) r~~ ~~~~ ~~􀀔~~ ~~ 􀀎 􀀗 􀀠 r~~ ~~~~ ~~􀀔~~ ~~  \n􀁞 􀀐􀀘 􀁠 􀁞 ~~ ~~􀀘􀀗~~ ~~ 􀁠  \n11) 􀀖~~ ~~v~~ ~~􀀕~~ ~~~~ ~~~~ ~~~~ ~~ 􀀠 ~~ ~~ 􀀐 v~~ 􀀕 ~~~~ ~~􀀕~~ ~~v~~ ~~ 12) v~~ ~~􀀕v~~ ~~v􀀙􀀎v~~ ~~􀀗~~ ~~ 􀀠 v~~ 􀀕 ~~~~ ~~􀀙v 􀀎 ~~ ~~~~ ~~  \n􀁞 􀀐􀀔 , 􀀐 ~~ ~~􀀔􀀚􀀖~~ ~~ 􀁠 􀁞􀀖􀁠  \n13) bb~~􀀕 ~~~~ ~~􀀔􀀕b 􀀎 ~~ ~~􀀙~~ ~~b~~ ~~􀀕~~ ~~~~ ~~b􀀕􀀎~~ ~~􀀔􀀛b~~ ~~ 􀀠 􀀕~~ ~~b􀀐~~ ~~􀀗b~~ ~~ 14) b~~ 􀀕 ~~􀀘􀀎~~ ~~b 􀀠 b~~ ~~􀀎b~~ ~~􀀗 􀀎 b~~ 􀀕 ~~~~ ~~b  \n􀁞 􀀔 , ~~ ~~􀀔􀀔􀀗~~ ~~􀁠 􀁞 􀀐􀀘 􀁠  \n15) n~~ 􀀕 ~~􀀎~~ ~~􀀔~~ ~~􀀔􀀔~~ ~~n~~ ~~􀀎~~ ~~􀀖􀀓~~ ~~ 􀀠 n~~ ~~~~ ~~􀀘 􀀐 􀀗 16) n~~ ~~n􀀎~~ ~~􀀘~~ ~~ 􀀠 􀀕nn~~ ~~􀀎􀀎~~ ~~􀀗􀀔􀀓 􀀎 n􀀕􀀕n􀀎~~􀀕 ~~n􀀔~~ ~~n􀀛~~ ~~  \n􀀐 ~~ ~~􀀕􀀖􀀗~~ ~~􀁠 􀁞 􀀐 ~~ ~~􀀗􀀘~~ ~~ 􀁠  \n􀁞  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaitttuDdHwz2f","https://ap.wps.com/l/cbCaitttuDdHwz2f","pdf",25443,"English","# Solve each equation\n## Check for extraneous solutions","[{\"question\":\"What is the main task of this worksheet?\",\"answer\":\"Solve each rational equation shown in the numbered problems. Work through the equation and determine the valid solutions.\"},{\"question\":\"Why must you check for extraneous solutions?\",\"answer\":\"Rational equations can generate solutions that do not satisfy the original equation after algebraic steps, especially after clearing denominators. Checking ensures only valid solutions are kept.\"},{\"question\":\"How are the practice problems organized?\",\"answer\":\"The worksheet lists multiple numbered equations (1 through 16) under the prompt to solve each equation. Each problem follows the same overall requirement to verify solutions.\"}]","Rational Equations - Solve each equation - Check for extraneous solutions | PDF",1791426914]