[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-70026-es":3,"doc-seo-70026-110":31,"detail-sidebar-cat-0-es-110":93},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},70026,3985741905716,"Rowan","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",38,"Examen","Fracciones Algebraicas","Guía de ejercicios de matemáticas sobre fracciones algebraicas. El material propone comprobar equivalencias entre fracciones, calcular expresiones con fracciones, extraer factor común y simplificar, aplicar productos notables y descomponer en factores. También incluye simplificación mediante reducción a una sola fracción, resolución de ecuaciones con fracciones y operaciones algebraicas con expresiones racionales. Se aportan resultados (Sol.) para cada apartado a–h e incisos posteriores, enfocando la técnica paso a paso.","I. E.S. Arroyo de la Miel Dpto de Matemáticas  \nFRACCIONES ALGEBRAICAS.  \n1. Comprueba en cada caso si las fracciones dadas son equivalentes:  \na) x3x26~~ ~~ y ~~ ~~13~~ ~~ b) x2+x~~ ~~2~~ ~~x y ~~ ~~x~~ ~~+x1 c) x32x-x y ~~ ~~x~~ ~~3-2~~ ~~ d) 93xx2--39 y ~~ ~~3x1-3  \nSol: a) Sí; b) Sí; c) No; d) No  \n2. Calcula:  \n1 3 1 2 1 3 3 x 1 1  \na) ~~ ~~ + ~~ ~~ - ~~ ~~ b) ~~ ~~ - ~~ ~~2 + ~~ ~~2~~ ~~ c) ~~ ~~ - ~~ ~~ d) ~~ ~~ - ~~ ~~  \n3x 2x x 3x x 2 x x x-1 x-1 x +1  \nSol: a) ~~ ~~56x ; b) ~~ ~~4x~~ ~~+6~~ ~~x23 ; c) ~~ ~~-~~ ~~3-x1)-3 ; d) ~~ ~~x22-1  \n3. Saca factor común y luego simplifica:  \n5x + 5   x2-3x   x2 + x   12x   \na) b) c) d)  \n3x + 3 2x-6 x2-1 4 x2 + 2x  \nSol: a) 5/3; b) x/2; c) ~~ ~~xx-1 ; d) ~~ ~~2x6+~~ ~~1  \n4. Recuerda los productos notables, descompón en factores y simplifica:  \na) ~~ ~~xx2+-11~~ ~~ b) ~~ ~~(xx-2~~ ~~1-1)2~~ ~~ c) ~~ ~~x~~ ~~22x--44~~ ~~ d) ~~ ~~x2~~ ~~+x24-x4+~~ ~~4  x2-16   x (x + 2)   x2-6x + 8   x2-9   \ne) f) g) h)  \nx2 + 8x +16 x2 + 4x + 4 x2-9 x4-81  \nSol: a) x-1; b) ~~ ~~xx+-11 ; c) ~~ ~~x~~ ~~+22 ; d) ~~ ~~xx+-22 ; e) ~~ ~~xx+-44 ; f) ~~ ~~x~~ ~~2 1; g) ~~ ~~xx+-33 ; h) ~~ ~~x29  \n5. Descompón en factores el dividendo y el divisor y después simplifica:  \n x2 + 3x   x2 + 2x-3   x3 + 4 x2 + 3x   x2 + 2x-3  \na) b) 3 2 c) d)  \nx2 + x-6 x -x x2 + x-6 x2 + 4x-5  \nI. E.S. Arroyo de la Miel Dpto de Matemáticas  \nSol: a) ~~ ~~xx-2 ; b) ~~ ~~x23 ; c) ~~ ~~~~ ~~-+2x ; d) ~~ ~~xx~~ ~~35 ;  \n6. Opera y simplifica:  \na) 􀂧􀂨  4 - x 􀂷􀂸 : 􀂧􀂨  1 + 1 􀂷􀂸 b)~~ ~~x~~ ~~+~~ ~~2~~ ~~2~~ ~~ . x2-4  \n􀂩 x 􀂹 􀂩 x 2 􀂹 (x + 2 ) x  \nc) 􀂬􀂫􀂪 􀂧􀂩􀂨 ~~ ~~2x + x~~ ~~~~ ~~1 􀂷􀂹􀂸 : x - x~~ ~~~~ ~~1 􀂷􀂹􀂸 􀂺􀂼􀂻 . x  \nd)  x2 . 􀂧􀂨  2 :  1  􀂷􀂸 e) 􀂨􀂧  3  + x + 2 - x +1 􀂷􀂸 . 2 x2  \n2 􀂩 x x + 2 􀂹 􀂩 x2 x x-2 􀂹 Sol: a) 4-2x; b) ~~ ~~xx-2 ; c) 3x+2; d) x2+2x; e) - ~~ ~~xx22+(xx-+22)  \n7. Reduce a una sola fracción y resuelve:  \na) - x2  +  2  -  2  = 0 b)  x + 3  -  2  -  2  = 0 x +1 x-1 x2-1 x2-2x +1 x-1 x +1  \nc)  x + 2 + x +1 - x + 5 = 0 x +1 x + 2 x + 2  \nSol: a) x=2, x=0; b) x=3, x=-1/3; c) x=0  \n8. Haz las operaciones indicadas y simplifica:  \na) 􀂧􀂩􀂨 ~~ ~~xx+-yy - xx+-yy 􀂷􀂹􀂸 . 􀂨􀂧􀂩 xy - yx 􀂷􀂹􀂸 b) 􀂧􀂩􀂨 ~~ ~~1x - 1y + x+xyy 􀂷􀂹􀂸 . x2yy  \n􀂧 x +1 x 􀂷 􀂧 1 􀂷  \nc) 􀂨 ~~ ~~ - ~~ ~~ 􀂸 . 􀂨 x - ~~ ~~ 􀂸  \n􀂩 x-1 x +1 􀂹 􀂩 x 􀂹  \nSol: a) 4; b) ~~ ~~xy ; c) ~~ ~~3xx+~~ ~~1  \n9. Resuelve las siguientes ecuaciones:  \na)  1 + x -  x  = 3x + 5 x2  b) x  +  3  = x +1  \nx-3 x + 2 x2-x-6 x-1 x +1 x2-1  \nI. E.S. Arroyo de la Miel Dpto de Matemáticas  \nc)  x2  = x + 2 - 2 d)  x +1 +  x  = 7x + 2  \nx2 + 2x +1 x +1 x-2 x + 2 x2-4  \nSol: a) x= 1, x=-2/5; b) x=0, x=-1/2; c) x=-4; d) x=3, x=0  \n10. Opera:  \n1 1 x-1 1 3 x +1  \na) ~~ ~~ + ~~ ~~ - ~~ ~~2~~ ~~ b) ~~ ~~ + ~~ ~~ - ~~ ~~2~~ ~~  \nx-1 x-3 x -4x + 3 x + 2 x-1 x + x-2  \nx 3 x-1 x 3 x + 2  \nc)  x2-x-2 - x +1 - x2-3x + 2  d)  x2-1 - x +1 - x2 + x-2  \nSol: a) ~~ ~~x~~ ~~1-1 ; b) ~~ ~~x32+x4-2 ; c) ~~ ~~x-23-xx+-52 ; d) ~~ ~~2x2-~~ ~~-3x1  \n11. Simplifica:  \nc)  \nx2 − 1 x + 1  \n2x 2 +14x + 20 x − 5  \n~~ ~~ : ~~  ~~x3 − 50 + 2x2-25x 2 x3-20 x2 + 50x  \nd)~~ ~~x~~ ~~22x22x~~ ~~+~~ ~~1~~ ~~xx+-11~~   ~~ : ~~  ~~x2 + x-2 x3-4 x2-7x + 10  \n􀂨􀂧 ~~ ~~x3-6~~ ~~x22+11x-6 . x22~~ ~~+~~ ~~2x-3~~ ~~ 􀂷􀂸 : ~~ ~~x22~~ ~~+~~ ~~x-2~~ ~~  \ne)  􀂩 x -9 x -3x + 2􀂹 x + 4x + 4  2 x2-2x 3 x2 +12x +12  \n_  \n3 x2 + 3x-6 2x  \ng) 􀂩􀂨􀂧 ~~ ~~x3~~ ~~+x2~~ ~~x-6x _ ~~ ~~x3~~ ~~26~~ ~~x-2~~ ~~9x~~ ~~ 􀂷􀂹􀂸 : ~~ ~~x2x-2+x~~ ~~6  \na2-1 a2 +1  \ni) ~~ ~~a2a+-11~~ ~~--~~ ~~aa-11~~ ~~ : 􀂩􀂧􀂨 a2~~ ~~1 _ aa-~~ ~~-2a1~~ ~~1 􀂷􀂹􀂸 a +1 a-1  \nx-3 1 + ~~  ~~f)  x + 3  \n3-x 3x  \n1 + x  \nh) ~~ ~~2~~ ~~y2~~  ~~x -y  \n2 xy-y  \na +b  \n1 + ~~  ~~j)  a-b a +b  \n1 - ~~ ~~a-b  \nx + 3 x + 3 -  \nx 3  \nx + 3  \n_  \nx-3  \n- 1  \nI. E.S. Arroyo de la Miel Dpto de Matemáticas  \nSol: a) 1; b) ~~ ~~x4~~ ~~2-x1+(5x-x~~ ~~24)+1(x)18 ; c) 1; d) 1; e) 1; f) ~~ ~~x~~ ~~(x3-3) ; g) 1;  \nh) 1; i) ~~ ~~(~~ ~~a221~~ ~~)2 ; j) - ~~ ~~ab 12. Simplifica:  \na) ~~ ~~a2~~ ~~+a26-a9+~~ ~~9~~ : ~~aa24-+891~~ ~~ b) ~~ ~~2~~ ~~a2-4a3x-b6+~~ ~~2~~ ~~b2 : a4x--b8 c) ~~ ~~164x~~ ~~x~~ ~~48 : (32-8 x2 ) = d) ~~ ~~","cbCaicNtUek2qkTd","https://ap.wps.com/l/cbCaicNtUek2qkTd","pdf",1224836,10,1,6,"Spanish","es",110,"# Ejercicios: equivalencia de fracciones\n# Cálculo y simplificación de expresiones\n# Factor común y productos notables\n# División de polinomios: dividendo y divisor\n# Operaciones y reducción a una fracción\n# Resolución de ecuaciones\n# Operaciones adicionales y simplificación","[{\"question\":\"Cómo se comprueba si dos fracciones algebraicas dadas son equivalentes?\",\"answer\":\"Se realiza el análisis de cada caso y se verifica la equivalencia según el resultado indicado en “Sol: a) Sí; b) Sí; c) No; d) No”.\"},{\"question\":\"Cómo se resuelven ecuaciones que incluyen fracciones algebraicas?\",\"answer\":\"Se reduce la expresión a una sola fracción y luego se resuelve la ecuación resultante; los ejercicios incluyen “Reduce a una sola fracción y resuelve” con soluciones para cada inciso.\"},{\"question\":\"En las operaciones con fracciones, qué procedimiento guía el ejercicio?\",\"answer\":\"Se realizan las operaciones indicadas (suma, resta, producto o división) y después se simplifica el resultado hasta llegar a la forma final indicada en “Sol”.\"}]","Fracciones Algebraicas | PDF",1784018807,9,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":29},"algebraic-fractions","",{"@graph":37,"@context":87},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/es/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/es/document/examen/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/es/document/algebraic-fractions/70026/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-15","2026-07-14",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"Cómo se comprueba si dos fracciones algebraicas dadas son equivalentes?","Question",{"text":77,"@type":78},"Se realiza el análisis de cada caso y se verifica la equivalencia según el resultado indicado en “Sol: a) Sí; b) Sí; c) No; d) No”.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"Cómo se resuelven ecuaciones que incluyen fracciones algebraicas?",{"text":82,"@type":78},"Se reduce la expresión a una sola fracción y luego se resuelve la ecuación resultante; los ejercicios incluyen “Reduce a una sola fracción y resuelve” con soluciones para cada inciso.",{"name":84,"@type":75,"acceptedAnswer":85},"En las operaciones con fracciones, qué procedimiento guía el ejercicio?",{"text":86,"@type":78},"Se realizan las operaciones indicadas (suma, resta, producto o división) y después se simplifica el resultado hasta llegar a la forma final indicada en “Sol”.","https://schema.org",{"og:url":53,"og:type":89,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":91,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":94},[95,100,104,106,110,114,118,122,126,130],{"id":96,"doc_module":4,"doc_module_name":47,"category_name":97,"show_sort_weight":98,"slug":99},39,"Cómic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":47,"category_name":102,"show_sort_weight":98,"slug":103},43,"Estilo de Vida","lifestyle",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":98,"slug":105},"exam",{"id":107,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":98,"slug":109},44,"General","general",{"id":111,"doc_module":4,"doc_module_name":47,"category_name":112,"show_sort_weight":98,"slug":113},41,"Investigación e Informes","research-report",{"id":115,"doc_module":4,"doc_module_name":47,"category_name":116,"show_sort_weight":98,"slug":117},37,"Literatura","literature",{"id":119,"doc_module":4,"doc_module_name":47,"category_name":120,"show_sort_weight":98,"slug":121},22,"Relatos y Novelas","story-novel",{"id":123,"doc_module":4,"doc_module_name":47,"category_name":124,"show_sort_weight":98,"slug":125},42,"Religión y Espiritualidad","religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":47,"category_name":128,"show_sort_weight":98,"slug":129},40,"Salud y Atención Médica","healthcare",{"id":131,"doc_module":4,"doc_module_name":47,"category_name":132,"show_sort_weight":98,"slug":133},24,"Tecnología","technology"]