分式及其运算(习题)例题示范例1:若代数式x2有意义,则x1x的取值范围是__________.【思路分析】由题意得,x2≥0x1≠0解得,x≥2且x≠1例2:分式的运算:【过程书写】6aa.2a+2a8a2解:原式6a(a2)(a4)a(a4)(a2)(a4)a24a6a(a2)(a4)a22a(a2)(a4)a(a2)(a2)(a4)aa4巩固练习下列各式:①114xx2y21.15x;②3;③2;④xx其中属于分式的是_________________.(填写序号)2.下列运算正确的是()A.b1ab1aB.x2yxxyC.xyyxyxyxyxD.xy13.下列各分式中,属于最简分式的是()5x2x;⑤.A.34(xy)85(xy)B.y2x2xyC.x2y2x2yD.x2y2xy2(xy)24.下列结论:①无论x取何值,分式2xx21都有意义;②当x1时,分式x1x22x3的值为0;③若使x1x2x1x1有意义,则x的取值范围是④x12是分式.其中正确的是_____________.(填写序号)5.若代数式xx1有意义,则x的取值范围是______________【思路分析】(请参照例1填写)由题意得,__________________________且x≠2x≠1;.解得,_______________6.若分式x21x1的值为0,则x___________【思路分析】(请参照例由题意得,__________________________解得,____________7.计算:(1)xx2xxyyx2y;(2.填写)a12aa24a23a21);x26x92x62(3);29xx3x16m2m4m2(4)2;m2m82m4m2x29xx29x23xx26x9abbccababcac(5);(6);a1a2a(7)2;+a2a11a2(8)122;a29a)x2x1x1;(10xx12x211(9).【参考答案】巩固练习1.①④⑤2.D3.C4.①5.x≥0且x≠1思路分析:x≥0x10;6.-1思路分析:x210x107.(1)1y2(2)2a2(3)x2(4)-2(5)2(6)2a(7)1(8)2a3≥0且x1xx≠1;(9)(1x110)1x1