江西专版2020中考数学复习方案第一单元数与式课时训练04分式.docx

6课时训练(四)分式(限时:40分钟)|夯实基础|1.[2019·宁波]若分式1x-2有意义则x的取值范围是()A.x>2B.x≠2C.x≠0D.x≠-22.[2019·兰州]化简:a2+1a+1-2a+1=()A.a-1B.a+1C.a-1a+1D.1a+13.[2018·葫芦岛]若分式x2-1x+1的值为0则x的值为()A.0B.1C.-1D.±14.如图K4-1下面的计算过程中从哪一步开始出现错误()图K4-1A.①B.②C.③D.④5.[2019·河北]如图K4-2若x为正整数则表示(x+2)2x2+4x+4-1x+1的值的点落在()图K4-2A.段①B.段②C.段③D.段④6.[2019·北京]如果m+n=1那么代数式2m+nm2-mn+1m·(m2-n2)的值为()A.-3B.-1C.1D.37.[2018·南充]已知1x-1y=3则代数式2x+3xy-2yx-xy-y的值是()A.-72B.-112C.92D.348.[2019·北京]若分式x-1x的值为0则x的值为.9.[2019·吉林]计算y2x2·xy=.10.[2019·武汉]计算2aa2-16-1a-4的结果是.11.化简:2a2-8a+2-a=.12.[2019·青岛]化简:m-nm÷m2+n2m-2n.13.[2019·聊城]化简:1-1a+3+6a2-9÷a+3a2-6a+9.14.[2019·广东]先化简再求值:xx-2-1x-2÷x2-xx2-4其中x=2.15.化简式子a2-2aa2-4a+4+1÷a2-1a2+a并在-2-1012中选取一个合适的数作为a的值代入求值.16.先化简再求值:a2-2ab+b2a2-b2÷a2-aba-2a+b其中ab满足(a-2)2+b+1=0.17.[2019·高安一模]先化简1-1x-1÷x2-4x+4x2-1再从不等式2x-1<6的正整数解中选一个适当的数代入求值.18.[2019·江西样卷四]已知a2+4a=0先化简再求值:3a2-9+1a+3÷a2a-3.19.先化简:2x2+2xx2-1-x2-xx2-2x+1÷xx+1然后解答下列问题:(1)当x=3时求代数式的值.(2)原代数式的值能等于-1吗?为什么?|拓展提升|20.[2019·滨州]观察下列一组数:a1=13a2=35a3=69a4=1017a5=1533…它们是按一定规律排列的请利用其中规律写出第n个数an=.(用含n的式子表示)【参考答案】1.B2.A3.B[解析]若分式的值为0则x2-1=0且x+1≠0∴x=1.故选B.4.B[解析]xx-y-yx+y=x(x+y)(x-y)(x+y)-y(x-y)(x-y)(x+y)=x2+xy-xy+y2(x-y)(x+y)=x2+y2x2-y2.故从第②步开始出现错误.故选B.5.B[解析](x+2)2x2+4x+4-1x+1=(x+2)2(x+2)2-1x+1=1-1x+1∵x为正整数-12≤-1x+1<0∴12≤1-1x+1<1∴表示(x+2)2x2+4x+4-1x+1的值的点落在段②.6.D[解析]2m+nm2-mn+1m·(m2-n2)=2m+nm(m-n)+m-nm(m-n)·(m+n)(m-n)=3mm(m-n)·(m+n)(m-n)=3(m+n).∵m+n=1∴原式=3.故选D.7.D[解析]∵1x-1y=3∴y-x=3xy∴x-y=-3xy∴原式=2(x-y)+3xy(x-y)-xy=-6xy+3xy-3xy-xy=-3xy-4xy=34.故选D.8.19.12x10.1a+411.a-412.解:原式=m-nm·m(m-n)2=1m-n.13.解:原式=1-a-3+6(a+3)(a-3)·(a-3)2a+3=1-a-3a+3=6a+3.14.解:原式=x-1x-2·(x+2)(x-2)x(x-1)=x+2x.当x=2时原式=2+22=2+1.15.解:原式=a(a-2)(a-2)2+1÷(a+1)(a-1)a(a+1)=a+a-2a-2÷a-1a=2(a-1)a-2·aa-1=2aa-2.∵a≠-1012∴a=-2.当a=-2时原式=1.16.解:原式=(a-b)2(a+b)(a-b)÷a(a-b)a-2a+b=a-ba+b·1a-b-2a+b=-1a+b.∵(a-2)2+b+1=0∴a=2b=-1∴原式=-1.17.解:1-1x-1÷x2-4x+4x2-1=x-2x-1·(x+1)(x-1)(x-2)2=x+1x-2.∵2x-1<6∴2x<7∴x<72∴不等式2x-1<6的正整数解为123又∵x≠1且x≠2∴选x=3代入上式得:原式=3+13-2=4.18.解:3a2-9+1a+