訓(xùn)練案.doc

2.分式的基本性質(zhì)1.下列變形錯誤的是(B)(A)ab=acbc(c0)(B)x2+yx=x+y(C)a-bb-a=-1 (D)axbx=ab2.下列分式中,分子、分母不含公因式的是(B)(A)a-bb-a(B)a2-b2a2+b2(C)2b6a(D)3b+3b2+2b+13.(2016濱州)下列分式中,最簡分式是(A)(A)x2-1x2+1 (B)x+1x2-1(C)x2-2xy+y2x2-xy(D)x2-362x+124.(2016黃岡中學(xué)質(zhì)檢)下列約分正確的是(C)(A)x6x2=x3(B)x-yx-y=0(C)x-yx2-xy=1x(D)2x2y4xy2=125.(2016勝利一中模擬)若分式2x-y3x2y的x和y均擴大為原來的10倍,則分式的值(C)(A)不變(B)縮小到原分式值的110(C)縮小到原分式值的1100(D)縮小到原分式值的11 0006.(2016重慶校級月考)分式a2b-ab2a3-ab2可化簡為ba+b.7.不改變分式的值,使下列分式中的分子、分母都不含有“-”號:(1)3a-4b=-3a4b;(2)-2x3y=2x3y;(3)-3n-4m=-3n4m;(4)-x-yx+2y=-x+yx+2y.8.(1)a+ba=a2-b2a2-ab;(2)0.5m-nm+0.1n=5m-10n10m+n.9.約分:(1)-3xy26x2y3;(2)3-aa2-9;(3)x2-2xx2-4x+4.解:(1)-3xy26x2y3=-3xy213xy22xy=-12xy.(2)3-aa2-9=-(a-3)(a+3)(a-3)=-1a+3.(3)x2-2xx2-4x+4=x(x-2)(x-2)2=xx-2.10.通分:(1)x6ab2,y9a2bc;(2)a-1a2+2a+1,ba2-1;(3)ba-b,a(b-a)2.解:(1)因為最簡公分母是18a2b2c,所以x6ab2=x3ac6ab23ac=3acx18a2b2c;y9a2bc=y2b9a2bc2b=2by18a2b2c.(2)因為最簡公分母是(a+1)2(a-1),所以a-1a2+2a+1=(a-1)(a-1)(a+1)2(a-1)=(a-1)2(a+1)2(a-1);ba2-1=b(a+1)(a+1)(a-1)(a+1)=b(a+1)(a+1)2(a-1).(3)因為最簡公分母是(a-b)2,所以ba-b=b(a-b)(a-b)(a-b)=b(a-b)(a-b)2;a(b-a)2=a(a-b)2.11.(探究題)當a,b滿足什么條件時,分式ab-a2ab-b2的值為正?解:ab-a2ab-b2=a(b-a)b(a-b)=-ab.當-ab0時,ab0,即a,b異號,所以當a,b異號時,ab-a2ab-b2的值為正.12.(整體思想)已知xy=3,求x2+2xy-3y2x2-xy+y2的值.解:法一由xy=3,可得x=3y.所以原式=(3y)2+2(3y)y-3y2(3y)2-3yy+y2=9y2+6y2-3y29y2-3y2+y2=12y27y2=127.法二原式=(xy)2+2xy-3(xy)2-xy+1=9+23-39-3+1=127.13.(探究題)若分式2m+6m2-9的值為整數(shù),求整數(shù)m的可能取值.解:2m+6m2-9=2(m+3)(m+3)(m-3)=2m-3,