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5.3 分式的加减法一课一练基础闯关题组同分母分式的加减法1.下列运算正确的是()A.-xy+zy=-x+zyB.-xy+zy=z-xyC.a-bc-a+bc=0D.6x+3+2xx+3=6+2xx+3【解析】选B.A.-xy+zy=-xy+zy=-x+zy=z-xy,C.a-bc-a+bc=a-b-(a+b)c=a-b-a-bc=-2bc=-2bc,D.6x+3+2xx+3=6+2xx+3=2(3+x)x+3=2.2.计算m-2nmn+n-mmn的结果是()A.1nB.-1mC.1mnD.1【解析】选B.原式=m-2n+n-mmn=-nmn=-1m.【方法技巧】同分母分式相加减的方法(1)“把分子相加减”是指把各个分式的“分子的整体”相加减,即各个分子都应有括号,当分子是单项式时,括号可以省略,当分子是多项式时,括号不可以省略.(2)分式相加减运算的结果,必须化为最简分式或整式.3.(xx天津中考)计算aa+1+1a+1的结果为()世纪金榜导学号10164114A.1B.aC. a+1D.1a+1【解析】选A.aa+1+1a+1=a+1a+1=1.4.(xx武汉中考)计算xx+1-1x+1的结果为_.【解析】xx+1-1x+1=x-1x+1.答案:x-1x+15.计算:x2x-1-xx-1=_.【解析】x2x-1-xx-1=x2-xx-1=x(x-1)x-1=x.答案:x6.计算:(1)x-1x+1x.(2)3x2x-y-x+y2x-y.(3)3(x-1)2-3x(x-1)2.【解析】(1)x-1x+1x=x-1+1x=1.(2)3x2x-y-x+y2x-y=3x-(x+y)2x-y=1.(3)3(x-1)2-3x(x-1)2=3-3x(x-1)2=3(1-x)(x-1)2=-3(x-1)(x-1)2=-3x-1.7.计算代数式aca-b-bca-b的值,其中a=1,b=2,c=3.【解析】aca-b-bca-b=ac-bca-b=c(a-b)a-b=c.当a=1,b=2,c=3时,原式=3.题组可化为同分母分式的加减法1.下列计算正确的是()A.1a+1a=12aB.1a-b+1b-a=0C.m-na-m+na=0D.1(a-b)2+1(b-a)2=1(a-b)2【解析】选B.A.1a+1a=2a,此选项错误;B.1a-b+1b-a=0,此选项正确;C.m-na-m+na=-2na,此选项错误;D.1(a-b)2+1(b-a)2=2(a-b)2,此选项错误.2.(xx丽水中考)化简x2x-1+11-x的结果是()世纪金榜导学号10164115A.x+1B.x-1C.x2-1D.x2+1x-1【解析】选A.原式=x2x-1-1x-1=x2-1x-1=(x+1)(x-1)x-1=x+1.3.化简x2y-x+y2x-y的结果是_.【解析】x2y-x+y2x-y=x2y-x-y2y-x=x2-y2y-x=(x+y)(x-y)y-x=-x-y.答案:-x-y4.计算:(1)4x-2+x+22-x.(2)a+2ba2-b2+bb2-a2-2aa2-b2.【解析】(1)4x-2+x+22-x=4x-2-x+2x-2=4-(x+2)x-2=-1.(2)a+2ba2-b2+bb2-a2-2aa2-b2=a+2ba2-b2-ba2-b2-2aa2-b2=a+2b-b-2aa2-b2=b-a(a+b)(a-b)=-1a+b.5.先化简,再求值:a2-2aba-b-b2b-a,其中a=1+3,b=-1+3.【解析】原式=a2-2ab+b2a-b=(a-b)2a-b=a-b,当a=1+3,b=-1+3时,原式=2.化简:2xy2+1(x-y)2-1+2x2y(y-x)2.【解析】2xy2+1(x-y)2-1+2x2y(y-x)2=2xy2+1-1-2x2y(x-y)2=2xy(y-x)(x-y)2=2xyy-x.【母题变式】变式一化简:(a+b)2a2+b2-2aba2+b2.【解析】(a+b)2a2+b2-2aba2+b2=a2+2ab+b2-2aba2+b2=a2+b2a2+b2=1.变式二化简:x+2yx2-y2+3y-xy2-x2-3x-4yx2-y2.【解析】原式=x+2yx2-y2+x-3yx2-y2-3x-4yx2-y2=3y-xx2-y2.
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