初中数学分式章节知识点及典型例题解析

初中数学视频教学集中地/shuxue7251、分式的定义：159a5abab21511x132222-、、、、am、、、、y2xy46x22x31、a））2）35xym.2x7x5x1a2xx2b222⑴；⑵.23ab2a3y3y7xxxy1b.；；；；；5x2482xy452、分式有，无意义，总有意义：0x21例x）12x12x____例xx51x例xx21x12xyxy例：，yx例x）x3xx5．x212x1x31x2x2x2x2x2．例x．x．．x2x2例x2(xx初中数学视频教学集中地/shuxue7253、分式的值为零：012aa1x12例x0例x0x1a2a22例例则a()x2x1（x）x20x1x0x1x0x1D或AxBC或x92例x零x25x6a10例则a(a4、分式的基本性质的应用：0AACAACC0BBCBBCxy6x(yz)yz)2a5aaby例：例：；则a；a721()a()a3b3ababa和b倍）10x例y）xy1倍例2倍xyx和y2）xy4D2倍初中数学视频教学集中地/shuxue725xy例x和y2）xy24D2倍xy例x和y2）xy124的y6倍D倍2x3y2x例倍）倍例y2）3x2y3x3x23x3、、、、2y2y2y22a例）abaaaaABCDabababab0.2x例；x1x=例。1xx25、分式的约分及最简分式：1baabbaxyxy1）））中y2xycaacabxyxyx2B2个、3个、4个、例）xx62xyxyxy12xy21x3；0、、；、；xxyx4xy222例()2xy2xyayyzyzcdcdcdcd010Aayxxxaaa例）初中数学视频教学集中地/shuxue725aa241a2ab111、、、、ababxx22mmmb2例）bbaa22abababab0.1abab01．．．．0.2ab2abm2mmmmm例A、、、9mm3m3m32114xy3x1253例例；=；；。6xy9x22a42xy＝；；；16xyx2a4a422ay16x914abc3x222；；xyx2x16x621a2239m2m35x92。20ab6x92x2a2ab1例1个，a3ab，，12(ab)x2()2222个3个4个6、分式的乘，除，乘方：ac〃=bd.acad÷=〃=bdbcan()nba()=abnn)nb）26x25x16xy56x124344aa））15x639y125a10100a13a7初中数学视频教学集中地/shuxue725ababax2x41a1a22242））））））aax5xa4a4a222224xbxyx22xy6xy6ab22）3y2axy32x5y10yx12x3a1a2a122x)a1））x222a12a63a2））a2a44aa2222x222xx222112x3xy2yx2xyy3xy(2y)2533ay23）3）=）=3x2x2323b22ab）=）42aba2a222）a2xyyzxzx求yzx2222xx2102530xy求2xy2yx2yxx211(xy)x2yB2ACDyxy1yxx22yx1yxxD.x1yxy2x8xx2x2x122x2a2a1322））a÷xx122122aaax24x424x12初中数学视频教学集中地/shuxue7257、分式的通分及最简公分母：2xx2x2。x2x2422xx2xx2x2x42x22xx22x2xx2112,,例）mnmnmn22(mn)(mn)(mn)(mn)(mn)mn．．22．222．222yx1，，）y2２２2３２x1xyx1xy222,,,x1x2y2x222211a例，.2a4a241例a与；b11,例。x2y2x2xy8、分式的加减：初中数学视频教学集中地/shuxue72522n2a3a422mm例：例：=例：=a1a122yxy=例：=xyyxx222224m1abab2））））m3m3abba5ab3ab58ab222－－.ab2ab2ab2135111例++2x．2x．6x．6x）．x2x3xbca2a13xxabc例：例：a4a2(x23x2xx612a1aaa2aa1例：－x2a24a122例：x2x1b14x12）））+.2xx42xa293a222b2xy2xyyxa11a2a1a111Da例aABCa1a1a112x例.x2x42x12x2430例xx求x2x4x42初中数学视频教学集中地/shuxue7259、分式的混合运算：42x1x3x2x12例：例：例：例：4x4x112xx4322xxxx2x2x)2x24x(22x2x23x1xx1xxyxy221例：1例：1xx1x2y22x112y()x1xxyxyx2y22例7例：xxx2x1x22x2x1x4()例：22x2xx4x4x10、分式求值问题：222x例x++x.x33xx291242411÷.2()()xyxy22xyxy1例x．2x1a3a2a12例a.1aa3a1a221x18112142求．．．．x31042x112x14xy2yx2xyy例3xya1a3a6a92例．aa3a2a24初中数学视频教学集中地/shuxue725x24x8xa28aaab2））））x2a2a22abb21a12x2x1x4a）()；a4a4a2x2xx4x4222x3x5－2x4x2aa2aa22）()()其中a,b3aba2babab322221x121xx11、分式其他类型试题：234例，，567，，，38n1248xx,,,,例：8n项xxx2345是。例nm是（）（）mnBC.D1例与5x23x1132a☆＝x(x例☆bab22231．x1或（）．x．x或13344)xxB；ACx(x4223y7AB：）(y1)(yy1y2BABABAB．．A．．xyy2例2x3yx2y2x2y2初中数学视频教学集中地/shuxue725111nmnmn1例m则()例2222ｙ例111111①。=。=3n111141111=12、化为一元一次的分式方程：x1x；2x154与x1x2x。1.2例23＝。a(x232x11例xx1x2x33xx2例24x2x2xax4例x的方程1ax33xxa例xx21a初中数学视频教学集中地/shuxue7251x2例与的2；x2x3mxx1例mx1x2x2x2xbxxb2(a例xaax1x12a(a例x:例a,ababab2xax2x1(x2)(x22x1x2?xx2y2x222例:(xy)2xyxyx1xm例xmx2x1(xx143x21350x4xx1x(x1X1X1X225x42x5111xx2x5x62x43x62x1x1211x2x123133））x2x33xx292x21x13、分式方程的增根问题：xmx3k4xx32x32324x2xx例xmxm例：m取2x3x3xm22例xm。x3x3xkx0例k.4x1x1x1x1m例m31x4x4初中数学视频教学集中地/shuxue7253a4例0）x2xx(x20或2114、分式的求值问题：a1ab例；b32ab11例。a1b1113a例a；2aa2113xy5xxy5y72例ABCxxyyxyy2例2x3yx2y2x2y2a例a2b2=ab2b2ab4x例例与,b=、yx。x2411x2x21xy0yx（、11xy1x24x（x3x3”例x2x4x4223x1例－a12”a1ax2x1x12xx2007x2007x1xx22成x1x23xxx1x4215、分式的应用题：初中数学视频教学集中地/shuxue725v=v+v．v=v-v．:水水例xy例6打x）ABCDx6xx6xxx6x例;期32为x()2x2311x2x31x1;21;1;xx3xx33xxxx3例ab11ab1b）a）））abab例x）1、、、、xxxx例x32xxxx）3333ABCDxxx2xxx2例31x1x；x3xx3．②3x例2例32例5初中数学视频教学集中地/shuxue725例6工4例6253例3x为（）3333．．．．xx2x2xxx2例31x．例2例例4)例17.581例年5月7824初中数学视频教学集中地/shuxue725例BABBA94x）99499、、、、x4x44x4xxx4x4例）=、B、=、、x2x2x2x2xxxx例3例VV12）vvvv12vv2vv12vv、、、1221212例abab）bbabababa倍倍倍倍bab例BAB3例BA3A3B例1例.4例例例816、公式变形问题：111UVF例U、VF）初中数学视频教学集中地/shuxue725UV）UVUV）））UV111RRRRRR1例（）1212RRRRR(RR)RRR1R1R1R1．．．．2RR2122RRRRR2222例vf111＋＝.若68＝.uvf1S(ab)h,例h）22S2S2SShabbah．abhh11ab例M,N1a1b1a1b>NN<N.初中数学视频教学集中地/shuxue725UV）UVUV）））UV111RRRRRR1例（）1212RRRRR(RR)RRR1R1R1R1．．．．2RR2122RRRRR2222例vf111＋＝.若68＝.uvf1S(ab)