分式的化简求值经典练习题(带答案)11184.pdf

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1、精心整理精心整理分式的化简内容基本要求略高要求较高要求分式的概念了解分式的概念，能确定分式有意义的条件能确定使分式的值为零的条件分式的性质理解分式的基本性质，并能进行简单的变型能用分式的性质进行通分和约分分式的运算理解分式的加、减、乘、除运算法则会进行简单的分式加、减、乘、除运算，会运用适当的方法解决与分式有关的问题一、比例的性质：比例的基本性质：acadbcbd，比例的两外项之积等于两内项之积.更比性（交换比例的内项或外项）：()()()abcdacdcbdbadbca交换内项交换外项同时交换内外项反比性（把比例的前项、后项交换）：acbdbdac合比性：acabcdbdbd，推广：acak

2、bckdbdbd（k为任意实数）等比性：如果.acmbdn，那么.acmabdnb（.0bdn）二、基本运算分式的乘法：aca cbdb d分式的除法：acada dbdbcb c乘方：()nnnnnaaaaa aaabbbbb bbb个个n个(n为正整数)整数指数幂运算性质：mnm naaa(m、n为整数)()mnmnaa(m、n为整数)()nnnaba b(n为整数)mnm naaa(0a，m、n为整数)知识点睛中考要求n1nnaa(0a)na(0a)naababcccacadbcadbcbdbdbdbd.12111xxx2x22010111xx xx x111xx xx2x112x122

3、2221()111aaaaaaa3a2222221(1)()4111(1)aaaaaaaaa4322144(1)1aaaaa1a220102221144211122a aaaaaaaaaaa1a112123aa1342291333xxxxx13x.2201033133xxxx x13x33 5211(1)(2)11xxx6x.22010111121xxxxx6x26244 622121(1)24xxxx5x2201022121(1)24xxxx=221(1)2(2)(2)xxxxx=21(2)(2)2(1)xxxxx=21xx5x21xx521512.127532224xxxx23x22010

4、2453(3)(3)2(2)22(2)22(3)3xxxxxxxxxx23x2 2228231124aaa23a220102223221aaaaaa2a912x22226124111xxxxxxxx32224(1)1(1)(1)2413xxx xxxxxxx131022222936931aaaaaaaaa0123a22010223332313aaa aaaaaaaaa0 1 2 3a0 2 4 60246 1122222ababbaaaba1b22aa2201022221ababaabbabaa abaaabab22aa1 0 11b1a222abaab0a22abba1a1abaa12212

5、242xABCxxxABCABC3x3201021221242222xxxABCxxxxxxx3x113221212124222xABCxxxxx xx3x133x11323x1313:224125(2)22()(34)(2)aaaaaaaa4a32224(3)5(2)(2)2(34)(2)aaaaaaaa4(3)(2)(2)5(34)(2)2aaaaaa4a441(34)(3)(344)(43)2aa:121420102009xy22xyyxyxxx2201022xyyxyxxx2010 x2009y=201020091xy1 152323ababba220102323ab4ab2 3ab1

6、ababba22()()abab ababababba()()ab abab42 31388316xyy xyx xy2121xy2201022xyxy xyxy xy2121xy2 1711-a bbaabab.21a,2b.320102baabababbaabab b212ab212b2222212221822112bababaabb1212ab3201022ababababababbab1212ab2222 22221922211x yxyxyxy3131xy320102222222xyxyx yxyxyxy3131xy2221313131xy1 2022222222222abcabca

7、bacaaabababab1a12b23c322222222222abcabcabacaaabababab2a bcaabcabcababa ababcabcababcab1a12b23c1212311213132631331.212244abab0ab22225369ababbabaabbab320102244abab2ba2abab2ba42aaaa1122x y z235xyzzx52xyyzA.1B.13C.13D.1242007B235xyzzx332yx zx55312333xyxxyzxx132334xy2222222xyxyyxxyyxxy32222222()()()32()(

8、)4xyxyyxyxyy xyxxxyyxxyxyx xyy3424220 x222(1)11xxxx22010=22(1)1)(1)1xxxxx=2111xxxx=211xxx220 x22x=211111xxxx12512xy2222222xxyyxxyyxyxy22010yxyyxyxyxyxx22222222()()xyxy21yxxy2.2(2)6(2)xxxx.626221547280 xxyyxy.3221547280 xxyy(37)(54)0 xyxy370 xy540 xy:0y73xy45xy.452722690 xxyy2235(2)4xyxyxy.3201022690

9、 xxyy2(3)0 xy3xy35(2)(2)(2)xyxyxyxy14514528512x351xxx4215x21xx0 x233245555111512xxxxxxxxxxxx5122920 xy22()2xyxyyxxxyy3201022()2xyxyyxxxyy=22222xyxyxyxxyy=2()()()xyxyxyxyxy=xyxy.20 xy2xy.xyxy=2332yyyyyy.3.3 303ab23acabcabc.312,33aabc123331233aaaabcabcaaa23ab223233acbb32332abcbbbabcbbb331123abcaccab48

10、23bcaaca22bcaca02bca220caaba2 322232abab0a0b252abab422230aabb(3)()0ab ab3abab0a,0b3ab23255322ahbbbabbbb52332232abab2abab.3()(3)0ab abab3ab212abab52.12523422(3)0 xyab32223322232332a xab yb xya xab yb xy3912yx3ab7297.7297351xyxymxynmn31.1xymxyxynxy11xyxynmxyxymn0mnmnmn36233mxy22201nxyxyxymn40 x233mxy2

11、3 1133yyymxx222nxy222 122yynxx1y0n23 112 1yyymnxx23 112 1yyxxy312xy312xy37230abc3260abc0abc3332223273abcabbca c.42303260abcabc43acbc333322233215173453abccabbca cc1338:230230 xyzxyz(0 xyz):x y z3zxy5yz7xz:7:5:1xy z.:7:5:1xy z394360 xyz270 xyz(0 xyz)222222522310 xyzxyz.343627xyzxyz32xzyz13.1340 xymn58

12、xymymnxymn558xy58ym85my864525nmyy825200200y1157 41a b c00abc222222222111bcacababc_419960abc2222abc aabbc2222abcab.22222222bcabc cabca.11102222abcbccaababc0 42abc11abc1111317abbccaabcbccaab5200811abc11111bcabcbcbccababbcca13921131717921743a b c0abc13333abcabc29abbccacabcababbcca5200510abcabc33abc3223

13、333aa babbc333333abcab ababcabc22211abbccacbccacccababababab221abbccaaacabbcbc221abbccabbcabcaacabbccacabcababbcca9 244234xyz222xyzxyyzzx_32234xyzkxk3yk4zk222222491629612826kkkkkk292645abcdbcdaabcdabcd.4abcdkbcdadak2cdkak3bckak4abkak41k1k.1k0abcdabcd1k2abcdabcd.0246()()()()()()(2)(2)(2)(2)(2)(2)yx z

14、xzyxyxzyzxyzxyzxyzyzxyzx xyz5xyayzbzxc2()()xyzxyyzab2()()xyzyzzxbc2()()yzxzxxyca.()()()()()()caabbcab bcbc cacaab()()()()()()ca caab abbc bcabbcca222()()()()()()cabc abab abab bc ca()()()1()()()abcacbabbcca.1 47222222()()()(2)(2)(2)bccaabbcacababc222(1)(1)(1)(1)(1)(1)bccaababc.5,abx bcy caz222222()(

15、)()xyzzxxyyz2222220 xyzxyyzzx.0 xyzabbcca2222220 xyzxyyzzx.22200 xyzxyzabc.222(1)(1)(1)1(1)(1)(1)bccaababc.1 48232332234abcbcacab2332abcabc=_.5232332234abcbcacabk232233324abckbcakcabk911ak811bk111ck.2343231abcabc.43149345xyyzzx222xyzxyyzzx=_.3345kxyyzzx345xykyzkxzk213xkykzk2221411xyzxyyzzx.1411501xy

16、zu2:12:22:3(2):4xyyzzuux733xyzu_52222234yzzuuxxyk(1)2(2)40 (5)xz(3)242 (6)zxk(5)(6)215xk815zk(1)(3)1115yk2915uk1xyzu281129311515151510kkkkk2037332310 xyzu2 51xyzxyzxyzzyx()()()xyyz zxxyz.5xyzxyzxyzkzyx(1)xykz(1)yzkx(1)xzky2()(1)()xyzkxyz0 xyz1k()()()8xyyz zxxyz0 xyz()()()1xyyzzxxyz.8152xyyzuzuxzuuxy

17、xyzxyyzzuuxzuuxxyyz5(13)()0kxyzu0 xyzuxyzuxyyzzuuxzuuxxyyz11 1140 xyzuxyzuyzuxxyyzzuuxzuuxxyyz111144453xyzbcacababc()()()bc xca yab z.5xyzkbcacababc()()()()()()()bc xca yab zcaabxca yab z()()()()2()()2()()0cayxabzxabca kac ab k.0 54abcxybxcycxayaxbyabc.0abc.5bxcycxayaxbykabc0 x(1)(2)y(2)(3)y(4)(5)k2

18、2220abcbcaabc0aabc0abc0559pqr222pqrxyzyzxzxypxqyrzxyzA.9B.10C.8D.7 511222pqrkxyzyzxzxy9pqr2229k xyzxyyzzx333pxqyrzk xxyzyxyz zxyz3333k xyzxyz9 xyz9pxqyrzxyzAA 562220(0)xyzyzxzxyxyzabc222abcbcacabxyz.6222xyzyzxzxykabc2xyzka2yzxkb2zxykc333(3)x xyzxyz.0 x0k233323abcxyzxyzxk.2233323bcacabxyzxyzyzk222abc

19、bcacabxyz.57222222222xyyzzxxyzyzxzxy222111111xyyzzxxyz69Axy Byz Czx0ABC222222ABCBCCAAB2222220ABCABBCCA0ABC22220ABCABBCCA2220ABC0ABCxyz2222222221111111111111xyzxyyzzxxyzxyz1 2.5820 xx2221412211xxxxxx.320102221412211xxxxxx=21(2)(2)(1)(1)2(1)xxxxxxx=(2)(1)xx=22xx20 xx22022xx25912abab_.baab220106601,12x

20、yxy222()3xyxyxy.222212222()172()()()333 1212xyxyxyxyxyxy71261210ab22()(1)()aababab2201052ab210ab21ab1162224aa121111122aaaaa22010211(1)1(1)(1)1aaaaa224aa22(1)a522563220 xx32331xxxx220105220 xx=2.2 643abab2()4()3()abababab.22()4()1410233()333abababab.10365210 xx222(1)(1)(1)121x xxxxxx32010222(1)(1)(1)

21、121x xxxxxx=2121(1)(1)11(1)xxxxxxx=11()11xxxx210 xx21xx=11 662380 xx21441212xxxxxx3201021(2)1212xxxxx2380 xx238xx3823103106712xy4xy1111xyyx.32222211(1)(1)2()2()2()2()23411(1)(1)()1()115xyxyxyxyxyxyxyyxxyxyxyxyxy341568210 xyxy4224xxyyxxyy.4422(2)20217242410462xxyyxyxyxyxyxxyyxyxyxyxy.7269111xyxyyxxy.

22、4111xyxy2()xyxy222()21yxxyxyxyxyxyxy1701114xy2322yxyxyxxy41114xy4()xyyx23232()12()2()22()2()8()yxyxxyyxyxyxyxxyyxxyyxyx.271113xy3237yxyxxxyy.4113xy3xyxy3233()21177()4yxyxyxxyxxyyxyyx.11472235xyyx2222410623xxyyxy.42222410623xxyyxy461023xyyxxyyx2321023xyyxxyyx251005.0 73111mn575232mmnnnmnm.4(1)111mn1n

23、mmnnmmn(2)0m0n(mn)274abc13abab14bcbc15cacaabcabbcca.511113114115abbcca1116abc1111116abcabbccaabbccaabcabc.167513xx221xx_4201077617xx221xx.417xx22127xx2219xx9 772213aa1aa.52213aa22121aa21()1aa11aa178x12xx441xx=_42422242111()2()222xxxxxx27915xx1xx.515xx22125xx22211()29xxxx13xx38011aa1aa.5222111()21aaa

24、aaa0a10aa222221111()221aaaaaaaa2213aa222111()2325aaaaaa15aa58112xx2421xxx.4200512xx21()4xx2212xx24222111131xxxxx.1313xx33441713xxxx=_5221137xxxx2323242421111772511502131xxxxxxxxxx1282a2310 xx5432225281aaaaa.5a2310 xx2310aa2235432322222(1)58252811(8)(39)311133aaaaaaaaaaaaaaaaa2310aa.183210 xx4521xxx4

25、422522221(1)214214253531(1)(21)(32)3253xxxxxxxxxxxx xx xxxxxxx210 xx.1 8421xaxx0a2421xxx50a0 x211xxxa111xxa422222221111121()1(1)1xxaxxxxxaa2242112xaxxa212aa85211xxmx36331xxm x.519940 x211xmxx11xmx2132m862710 xx1xx221xx441xx.52710 xx0 x2710 xxx17xx17xx221249xx22147xx22147xx44122209xx4412207xx22078725

26、10aa4221aaa.52510aa0a150aa15aa24882310 xx221xx.52310 xx0 x13xx22129xx2217xx72310 xx74843231xxxxx_52221131037xxxxxx23232424211113232501150131xxxxxxxxxx1 89210aa4232232932112axaaxaax.511aa2212()3931112()2axaaxa2(12)39312112xx1510 x1510902410aa42321533amaamaam.51714aa24223211145133123()amamamaamaamama3

27、72m372m9125342()xaxbxcxxdx1x11x4111x25342()11xaxbxcxabcxdxd1x25342()()111xaxbxcxabcabcxdxdd14.9210 xyzmnpmnpxyz222222xyzmnp519960mnpxyz0myznxzpxyxyz0myznxzpxy22222212121xyzxyzxyxzyzpxynxzmyzmnpmnpmnmpnpmnp19330 xyza a222xayayazazaxaxayaza_5123xyza0 xayaza2222xayazaxayayazazaxa.22212xayayazazaxaxayaza12941xyzt11111111xxyxyzyyzyztzztztxttxtxy.61121xyztxyzxxyxyzyyzyztzzttxttxtxy1 951xyzyzzxzy222xyzyzzxxy=_6xyz1xyzyzzxzyxyzxyzxyzyzzxzy222xyzxyzxyzyzzxzy2220 xyzyzzxxy.0