Multiplying and Dividing Rational Expressions

Transcription

1 Lesson Peview Pt - Wht You ll Len To multipl tionl epessions To divide tionl epessions nd Wh To find lon pments, s in Eecises 0 Multipling nd Dividing Rtionl Epessions Multipling Rtionl Epessions Check Skills You ll Need (Fo help, go to Lessons - nd -6) Simplif ech epession 0 b b b c c c 6 n n n 6 (- ) Fcto ech polnomil c + c + t - 6t + q + q + (c ± )(c ± ) (t )(t ) (q ± )(q ± ) Intective lesson includes instnt self-check, tutoils, nd ctivities Multipling tionl epessions is simil to multipling tionl numbes c c If, b, c, nd d epesent polnomils (with b 0 nd d 0), then b d bd - Pln Lesson Peview Check Skills You ll Need Multipliction Popeties of Eponents Lesson -: Emple Eecises Et Pctice, p 0 Fctoing Tinomils of the Tpe ± b ± c Lesson -6: Emple Eecises Et Pctice, p 0 Lesson Resouces Need Help Remembe tht the vlue of the epession in the denominto cnnot be zeo Check Undestnding Multipl b ( ) ( )( ) Multipling Rtionl Epessions Multipl 6 b Multipl the numetos nd multipl the denomintos Multipl the numetos nd multipl the denomintos Leve the nswe in fctoed fom ( )( ) ( ) c s with tionl numbes, the poduct bd m not be in simplest fom Look fo fctos common to the numeto nd the denominto to divide out Teching Resouces Pctice, Reteching, Enichment Reching ll Students Pctice Wokbook - Spnish Pctice Wokbook - sic lgeb Plnning Guide - Pesenttion ssistnt Plus! Tnspencies Check Skills You ll Need - dditionl Emples - Student Edition nswes - Lesson Quiz - PH Pesenttion Po CD - Check Undestnding Using Fctoing Multipl nd Fcto the denominto ( )( ) Divide out the common fctos 6 ( )( ) nd ( ± ) Simplif Multipl nd 6 Ongoing ssessment nd Intevention efoe the Lesson Dignose peequisite skills using: Check Skills You ll Need Lesson - Multipling nd Dividing Rtionl Epessions 6 Duing the Lesson Monito pogess using: Check Undestnding dditionl Emples Stnddized Test Pep fte the Lesson ssess knowledge using: Lesson Quiz Compute Test Geneto CD Compute Test Geneto CD Technolog Resouce Po CD-ROM Compute Test Geneto CD Pentice Hll Pesenttion Po CD wwwphschoolcom Student Site Teche Web Code: ek-00 Self-gding Lesson Quiz Teche Cente Lesson Plnne Resouces Plus 6

2 Tech Mth ckgound In ddition to ecluding vlues of the vible tht mke the function undefined, eliminting vlues tht do not ppl is pticull impotnt in ppliction poblems 6 Teching Notes dditionl Emples Multipl 6 b Multipl nd Multipl nd ( )( ) + + Teching Notes dditionl Emples Divide 0 b ( ± )( ± ) Divide b ( + 6) Closue 6 ( ) ( )( 6) sk students to eplin how to multipl nd divide tionl epessions To multipl tionl epessions, fcto ech numeto nd denominto, divide the numetos nd denomintos b n common fctos, then multipl the emining fctos of the numetos nd denomintos To divide tionl epessions, multipl the dividend b the ecipocl of the diviso nd poceed s bove Check Undestnding Pt Dividing Rtionl Epessions Reding Mth The vinculum o fction b is gouping smbol Check Undestnding You cn lso multipl tionl epession b polnomil Leve the poduct in fctoed fom Multipling Rtionl Epession b Polnomil Multipl s s nd s + s + 6 s (s + s + 6) s (s )(s ) s (s ) Fcto (s ) Divide out the common fcto s (s ) (s ) s ± (s )(s ) Leve in fctoed fom c d Recll tht b d b c, whee b 0, c 0, nd d 0 When ou divide tionl epessions tht cn be fctoed, fist ewite the epession using the ecipocl befoe dividing out common fctos Dividing Rtionl Epessions Divide 0 b Multipl b 6, the ecipocl of ( )( ) ( 6)( 6) 6 ( 6) Fcto ( )( ) ( 6) Divide out the common fctos ( 6) ( 6) ± nd 6 ( + )( + 6) Leve in fctoed fom 6 Chpte Rtionl Epessions nd Functions Reching ll Students elow Level Cution students tht onl common fctos of the entie numeto nd denominto cn be divided out Fo emple, - Multipl c c - c b v v v - v - c (m - ) (c )(c ± ) v(v ) (m ) m Dividing Rtionl Epession b Polnomil Divide b + ( )( ) ( ) Fcto ( ) ( ) ( ) Simplif 0 m m Divide b m 0 m c 6n n 6 b m 0 m 0 n n (m 0) n b (m 0) The ecipocl of polnomil such s n + is dvnced Lenes Hve students simplif n n Multipl b the ecipocl of ± Divide out the common fcto ± Eo Pevention See note on pge 6

3 Check Undestnding EXERCISES Pctice nd nd Poblem Solving Solving Pctice b Emple Emple (pge 6) Emple (pge 6) Emple (pge 6) Emple (pge 6) Emple (pge 6) ppl You Skills ( ) The student fogot to ewite the epession using the ecipocl befoe cnceling 6 nswes m v Smple: Divide - z b ( + ) c z (z - ) z z 0 0 ( ) z m(m ) Multipl (m )(m ) ( ) 0 6 t t t m m ( ) 6 6 m m ( ) ( ) c c c t t 6 c c c 6 t t t 0 m m 6 6 m m t t t - t - 6 m m - 6 m 6 - (t ± )(t ± ) (m ± )(m ± ) ( )( ) Find the ecipocl of ech epession d 6 6d c d - s + 6d c s Divide 0 See mgin 0 t t t 0t 0 6 n n n 6 n n n 6 ( + ) k (k + ) 0 ( - ) k Multipl o divide t t 6 t t t ± 0 c c t t t c c t t 6t t t 0 t t t t Eo nlsis In the wok shown t the ight, wht eo did the student mke in dividing the tionl epessions 6 Open-Ended Wite two tionl epessions Find the poduct Citicl Thinking Fo wht vlues of is the epession 6 undefined 0,, 6 Fo moe pctice, see Et Pctice Q RQ 0 0 R ( ) c c c c ( ) ( ) Lesson - Multipling nd Dividing Rtionl Epessions 6 pges 6 66 Eecises 0 6 ( ) 6 k n n See left Pctice ssignment Guide Objective C Coe,, 6, Etension Objective C Coe 6, 0, 0, 6 Etension Stnddized Test Pep Mied Review 6 Eo Pevention Eecises When ll fctos of the numeto nd denominto e eliminted, students m indicte vlue of 0 insted of Remind students tht Cees Eecises 0 lon office guides clients though the pocess of ppling fo commecil, consume, o motgge lon Lon offices must keep best of new tpes of lons nd othe finncil poducts nd sevices, so the cn meet thei customes needs Enichment - Reteching - Pctice - Nme Clss Dte Pctice - Find ech poduct o quotient Multipling nd Dividing Rtionl Epessions 6 6 b 6 0 m 6 m m b n 0n 6 n n 6n 6 b b b b b 0 b 6b b b b p 6 (h ) 0 p h h 0 p p h h 6h h n n n h h 6 n Two dts e thown t ndom onto the lge ectngul egion shown Find the pobbilit tht both dts will lnd in the shded egion 6 Lesson - Pctice lgeb Chpte Peson Eduction, Inc ll ights eseved 6

4 ssess Lesson Quiz - Multipl o divide 6 6 ( ± ) ( + + 6) ( )( ) ( ) 6 ( + + ) ± 0 ltentive ssessment Numbe five sets of inde cds ech fom to ( cds totl) Rndoml distibute the cds to the clss sk students to wite thei own tionl epessions modeling the emple whose numbe is on thei cd Students should wite thei epessions diectl on thei cds Collect the cds nd edistibute Hve ech student solve the epession on the cd She wote w s fction so she could esil see wht she could cncel Need Help If two events nd e independent, then P( nd ) P() P() Lon Pments The fomul below gives the monthl pment m on lon when ou know the mount boowed, the nnul te of inteest, nd the numbe of months of the lon n Use this fomul nd clculto fo Eecises 0 Wht is the monthl pment on lon of $00 t % nnul inteest fo months $ Wht is the monthl pment on lon of $000 t 6% nnul inteest fo months $6 0 Suppose ou pents wnt to bu the house shown t the left The hve $,000 fo down pment Thei motgge will hve n nnul inteest te of 6% The lon is to be epid ove 0-e peiod How much will ou pents hve to boow $00,000 b How mn monthl pments will thee be 60 pments c Wht will the monthl pment be $ d How much will it cost ou pents to ep this motgge ove the 0-e peiod $, Geomet Find the volume of ech ectngul solid ( ) 6 m Q RQ Rn Q Rn m m 6 m m m (m ) (m )(m ) 6 m m m m m ( )( ) Witing Robin s fist step in finding the poduct w ws to ewite the w epession s w w Wh do ou think Robin did this See left 6 Pobbilit If point is selected t ndom fom figue nd is equll likel to be n point in the figue, then the pobbilit tht the point is in shded e of shded pt pt of the figue is e of whole figue Suppose two points e chosen Wht is the pobbilit tht both points will be in the shded pt b Wht is the pobbilit tht one ( ) point will be in the shded pt nd the othe point will not be in the shded pt ( ) ( ) 660 Chpte Rtionl Epessions nd Functions 660

5 0 m (m ) ( b)( b) ( b)( b) (w )(w ) Stnddized Stnddized Test Pep Test Pep Multiple Choice [] ( )( )() ( ) ( ± ) [] one computtionl eo OR nswe with no wok shown Tke It to the NET Online lesson quiz t wwwphschoolcom Web Code: e-0 Shot Response b Multipl o divide (Hint: Remembe tht c c b d ) d m m (6m + m) t t t m m t t t t 0 b 6b b 6b 0 b b b m w m m ( ) w 6m m(m ) 6 ( ) w m w Simplif ( - ) 0 C D 0 Simplif G F - G ( ) ( H I ) ( ) 6 Which epession is equivlent to - D ( ) C D Q R 6 Which CNNOT be the fist step in multipling b G F Multipl the numetos G Find the ecipocl of 6 H Fcto ech polnomil I Multipl the denomintos Simplif Wite the poduct in fctoed fom Show ou wok See left Stnddized Test Pep Resouces Fo dditionl pctice with viet of test item fomts: Stnddized Test Pep, pp 6 6 Test-Tking Sttegies, p 6 Test-Tking Sttegies with Tnspencies Eecise 6 Remind students to multipl b the ecipocl of - pges 6 66 (, ) O 6 Eecises O 6 Mied Review (, ) Lesson - Simplif ech epession 6 6 Lesson - b b 6k 60 0 k k 6 q 6 q 6 t t q 6 z z 6 66 z 0 z 6z z 6 m m 6 6m m m m m c 6c c c c c ssume nd b e legs of ight tingle, nd c is the hpotenuse Find the length of the missing side of ech ight tingle If necess, ound to the neest tenth (, ) O 6, b 6, b 0!, c!!0, b!, b 0, b 6 Lesson 0- Gph ech function Lbel the is of smmet nd the vete 6 See mgin Lesson - Multipling nd Dividing Rtionl Epessions 66 66