分式章节综合训练(培优)例1:m=时,分式(m−1)(m−3)m2−3m+2的值为0.例2.要使分式没有意义,求的值.例3.若,的值扩大为原来的倍,下列分式的值如何变化?⑴⑵⑶例4.化简:例5.计算:1x(x+1)+1(x+1)(x+2)+1(x+2)(x+3)⋅¿¿例6.已知3x-4y-z=0,2x+y-8z=0,求的值.例7.已知|3a+b−1|+(5a−52b)2=0.求(−3ab)2.(ab3−a3b2)3÷(−6ba2.)2的值.课内练习:1.[23x−2x+y(x+y3x−x−y)]÷x−yx,其中5x+3y=02.若分式1−b2b2+1的值是负数,则b满足()A.b<0B.b≥1C.b<1D.b>13.如果分式|y|−3y2+2y−3的值为0,求y的值.4.下列各分式运算结果正确的是().①5a3b22c.10c5a3b4=25c4b2②b2c3a3⋅a2b=bc3a③1x2+1÷(x−3).1x−3=1x2+1④xy.x−1x2−1÷x+1xy=1A.①③B.②④C.①②D.③④6.1−3a2b−3a2b×2b2a等于()A.a−baB.b−abC.3a−2b3aD.2b−3a2b7.(1).a−ba+b−a+ba−b=______.(2).12m2−9+23−m+2m+3=______.8.化简:(1)(是大于1的整数);(2)(是正整数)9.把下列分式中的字母和都扩大为原来的5倍,分式的值有什么变化?(1)(2)10.2x(x+2)+2(x+2)(x+4)+2(x+4)(x+6)⋅¿¿11.为何值时,分式有意义?12.已知1x−1y=3,求分式2x+3xy−2yx−2xy−y的值.13.如果x,y,z满足x+y−5z=0,x−y+z=0,且xyz≠0,求x2−y2z2−x2的值.例2:已知(x≠0,y≠0),求xy−yx−x2+y2xy的值.例4.已知xx2+1=12,求x2x4+1的值.例5.若a,b为实数,且ab=1,求:aa+1+bb+1;1a+1+1b+1;1a2+1+1b2+1例6.已知x1+x2=3,x1x2=1,求:1x1+1x2;x1x2+x2x1;x2+1x1+1+x1+1x2+1例7.已知实数a,b,c为实数,且aba+b=13,bcb+c=14,cac+a=15.求abcab+bc+ca的值.例7.已知xx2−x+1=17,求x2x4+x2+1的值;例8.已知a2−3a+1=0,求下列代数式的值.(a−1a)2;a4+1a4;a4+a2+1a28.已知a+b+c=0,则1a2+b2−c2+1b2+c2−a2+1c2+a2−b2=()A.0B.1C.-1D.29.1a+1b=5a+b,则ba+ab=()A.5B.7C.3D.1310.已知2x−3x2−x=Ax−1+Bx,其中A,B为常数,那么A+B的值为()A.-2B.2C.-4D.411.已知2x−3x2−x−2=Ax−2−Bx+1,其中A,B为常数,求4A−B的值.15.已知x+1x=3,求x2x4+x2+1的值.16.求下列分式的值.(1)已知1x−1y=3,求5x+3xy−5y3x−xy−3y的值;(2)已知x2−5x+1=0,则x2+1x2=(3)已知1a+1b=4,则a−3ab+b2a+2b−7ab=18.分式的计算:(1)(a+2a2−2a+84−a2)÷a−2a(2)(−3yx)3÷(−9x4y)⋅(−x2y)4(3)2x−6x−2÷(5x−2−x−2)(4)a+2−42−a(5)(ba−ab)÷(1a−1b)(6)1x+2−x2+2x+1x+2÷x2−1x−1(7)(nm−2+mn)⋅(1+nm−nm−n)(8)a2+aba2−b2÷a2+2ab+b2a−b(9)3+2x2−x+3x−2x+2+x2−6x4−x2(10)a−b+2b2+2aba+b(11)(aa2−b2−1a+b)÷bb−a(12)(x−1x−1x)÷x−2x2−x(13)xx−2−x2+2x+1x+2÷x2−xx−1(14)(1a−b−1a+b)÷aba2−b219.化简求值:(1)已知a=1,b=−2,求(4a2−b2+a+bab2−a2b)÷a2−2ab+b2a2b−b2a的值;(2)n=−4,求5m−nn2−mn+nmn−n2−3mn2−mn的值.20若a+b+c≠0,2a+bc=2b+ca=2c+ab=k,求k和abc(a+b)(b+c)(c+a)的值.21.某人上山的平均速度为v1,下山的平均速度为v2(按原路返回),则上下上的平均速度为