Lesson30.pdf

1 Leson30Section6.1RationalExpresionsandFunctionsARationalExpresionisapolynomialdividedbyanon-zeropolynomial.Thefollowingarexam plesofrationalexpresions. 852 ,13 ,59 ,2 ,43 222 ?++?+ yyyrrrxxwARationalFunctionisafunctionwheref(x)isrepresntedbyartionalexpresion.1)Evaluatethefollowingrationalfunctionforthegivenvalues.forx=0,-2,3,and5 513)( 2?+=xxxxG ProcedureforSimplifyingRationalExpresion:I.Facteachdenominatorandnumerator.I.Youm ayncelthesam efctorfoundinanumeratorandadenominator,sincetheequalafctorof1.Youm yalsocancelafctorinanumeratorthatisoppositeofafctorinthedenominatorndthatquotientequalsfctorof-1.I.Thesim plifedrationalexpresionisthefactorsthatrem ain. Caution:CanclonlyFactors,nvrTerm s!!m m mSim plifyeachexpresion.2)3025 3) )52)(3( )3)(2( ?++?xxxx 2 4)baba332645) aa6123+ 6)yyyy63622+? 7) yyy1242042+? 8)xxx969422+? Rem m ber: Oppositerduceto-1 133?=? 1?=?xx 1?=?baab9) )2( )3)(2( ?+?xxx 3 ProcedureforMultiplyingorDividingRationalExpresionsandwritngtheproductorquotintinsim plifedform :I.Factoreachnumerat anddenominator.I.Cnclnyfactorthesm einthenumeratoranddenominatororoppositefactors.I.Multiplyacrossandlaveifactordfm .IV.Withdivision,m ultiplybythereiprocalofthedivisor. Multiplyordivide.Writeanswersinsim plifedform .10)2 32168 36aabb÷ 11)25612 4810mm??i 12)2 21156 25 56a aaaa? ?+i 13)22 233 4412xyyxxy x? ?÷+ 4 14)22 236318 81612y yyy yy? ?÷+ 15)2 22 32994932xx xxxxx++?÷ Department of Mathematics Lesson 31