write:(a)1x+1=152×4(b)x+3+3×1=4xx1SolutionOkay justlikewiththelinearequationsthefirstthingthatwe’regoingtoneedtodohereistoclearthedenominatorsoutbymultiplyingbytheLCD. Recallthatwewill

noticethatallwecandoforfactoringistofactoranxoutofeverything.Doingthisgives
x(5×2)=0Fromthefirstfactorwegetthatx=0andfromthesecondwegetthatx=25.Thesearethetwosolutionstothisequation.Notethatifwe’dcanceledanxinthefirststepwewouldNOThavegottenx=0asananswer!Let’sworkanothertypeofproblemhere.WesawsomeofthesebackintheSolvingLinearEqua-tionssectionandsincetheycanalsooccurwithquadraticequationsweshouldgoaheadandworkontomakesurethatwecandothemhereaswell.Example2Solveeachofthefollowingequations.(a)1x+1=152×4(b)x+3+3×1=4xx1SolutionOkay
justlikewiththelinearequationsthefirstthingthatwe’regoingtoneedtodohereistoclearthedenominatorsoutbymultiplyingbytheLCD.Recallthatwewillalsoneedtonotevalue(s)ofxthatwillgivedivisionbyzerosothatwecanmakesurethatthesearen’tincludedinthesolution.(a)1x+1=152x4TheLCDforthisproblemis(x+1)(2×4)andwewillneedtoavoidx=1and©PaulDawkinsAlgebra–101–