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1、分式加减法专项练习60题（有答案）22.a(a-1)+aaa+13:bfa+b42x_1x2-1x-15 .，+Z.a+1a2-16 .，-3X-3X(-3)7 .I4J=aa8 .a+1a+16yue28a2-b2a+bIi2m_1-4血2K2-2x_2+-2x2-4x2+4x+413.In-5in2m2in2-215. a-1-a2aa2-2a+la2-1(2)29x12-9x2+3xx2+6x+916. (1)12;m2-9m-32218.lnnd_nnm-2nK_4m+4n17.a-2a2_4ga2+ab+b2_b:;ab+b2a3-b3b2-2ab+b2a2-b220.1,1a-la
2、la2.121.x+1X2-IO23ID+2ml_2m2-lm-124.5-i，-l(-1)(x+2)29.（式中a,b,C两两不相等）：7-10x2-6x+82计算:26,+1.+2ro2-93-r11H-328.a+9b_a+3b3ab3ab2a-bc2b-c-a2c-a-b2+2+?a-ab-ac+bcb-ab-bc+accac-bc+ab30. 2x5x2+x-62-x-12231. (1)1-x+y；x+y(2) +，,X(x+l)(x+l)(x+2)(x+2005)(x+2006)32. b+2a+c_b-ca-b+cb-a-cba-c33. 化简分式：2a2+3a+2.a2-a-
3、5-3a2-4a-52a2-8a+5a+1a+2a-2a-334. 2+2yy2-2-2yy2*9222xy+yxy-y36三三37.计算:x+2y3y-X2_2+2_2XyyX3-4yT7Z39.计算化简:+-x2+3x+2x2+x-21-X241.计算40.计算:+,+工+_1_.I-Xl+2+4I-2_+12x2+3x-12X2+3x+12x2+3x+3242.计算：a+2a+l一(a-2).a+144.22xyy-y43.化简:x+y2-y2245.计算：-1.+.x2-yy-ZUOgUO55.化简:x2-l2x2+2x+1x+147.化简:2a-bc2b-c-a2c-a-b(a-b)
4、(a-c)+(b-c)(b-a)+(C-a)(C-b)48.2a-(a+1)+a3a+l2a+3a2-la2-lI7I551三-1250.计算：3x+5x+3x2+2x-352.计算：I-刍二史圣.53.计算：1+1aa2-1ab2ab54.化简2xr-Z+2yr-z+2z-x-yX2-xy-xz+yzy2-xy-yz+xzz2xz-yz+xy56 .先视察下列等式，然后用你发觉的规律解答下列问题：由一1二1二11二1.U1二1二1一-112-2-1223-6-2134-1231(1)计算，+，+，+，+，+，+，=(n为正整数)；12233X44X5566778(2) 化简：+,+X(x+l
5、)(x+l)(x+2)(x+2)(x+3)(x+2008)(x+2009)257 .化简：X+2x-_g_.60.求和x2-4X-258 .请你阅读下列计算过程，再回答所提出的问题：题目计算：工a+39-a2解：原式二工一力_6_（八）a+3(a+3)(a-3)二-(B)(a+3)(a-3)(a+3)(a-3)=a-9(D)(1)上述计算过程中，从哪一步起先出现错误：.(2)从B到C是否正确，若不正确，错误的缘由是(3)请你把正确解答过程写下来.59.视察下面的变形规律：，=I-1.，_二工-工工12223233434解答下面的问题：(1)若n为正整数，请你猜想,1、二n(n+l)(2)证明你
6、猜想的结论；(3)求和：+1+-+12233420112012参考答案：1 .原式二-二+广二+1=1+1=2.a-ba-b1a-bi2 .原式二a?-aa=a2-a+a=a2.a+14.原式二2x_1二-1_1(x+l)(x-l)x-1(x+l)(x-1)x+15.原式=，+_2a+1(a+1)(a-_a-1+2=1-1)(a+1)(a-l)a-16.原式二x-3-x-3=1x(x-3)x(:-3)xCx-3)X7.l2=l2=3aaaa8.原式=aIslJa+l)(a-l)=a-1.a+1a+19.:2xyx(x-y)=2xy+x2一y(x+y)(-y)(x+y)(x-y)(-y)(x+y
7、)(+y)_x(y)(x+y)xy20.a-ab+b=a(a-b)+b=a+b=a+b1.a2-t)2a+b(a+b)(a-b)a+ba+ba+ba+b11.原式=-=三t?二1.(rH-2)(m-2)(rd-2)(In-2)(rr2)(m-2)m2X(x-2)_(X-I)(x+2)=X_X-1_1(x-2)(x+2)(x+2)2x+2x+2x+213.原式三2(IrrH.)2m(In-I)(11H-1)m(In-5)2m(m-1)(rrl)m23m2_(m-1)(in-2)2m(m-1)(i-1)2m(In-I)(rrl)14. 原式二工+(1+a)(l-a)=/+1-/=.1+a1+a1+
8、a1+a15. V1_a2+a=a-l_a(a+l)二1_a=1.J_1a2-2a+la2-l(a-1)2(a-l)(a+1)a-1a-1aT16. (1)原式二12-2(严3)-2(m-3)二_(rH-3)(m-3)(11H-3)(In-3)(11r3)(2) 式二X(x+9)(x+3)(-3)_(x+9)(-3)_2x+6、x(x+3)(+3)2(x3)+(x+3)-x+314_a+24_a+2-4a-2(a+2)(a-2)(a+2)(a-2)(a+2)(a-2)(a2)(a-2)218.原式二119.29原式二小噤一(ab)(a2ab+b2)丑一11.(In-2n)二1_In-2n=mn
9、-(m-2n)-m+n-ro2n=3nm-2n(m+n)(m-n)11H-n11H-nmn11H-11b2.(a+b)(a-b)=1_b.1.b(a-b)2b(a+b)a-b(a-b)ab20.11_2a=a+l+a_1_2a-0a-1+a+la2-1(a-1)(a+1)(a+1)(a-1)21 .原式=(X-I)2_4x=(+l)2=+l,(x+l)(x1)(x+l)(x-1)(x+l)(x-1)x-122.原式二飞2xyxy)(x+y)y(+y)=y(-y)二y(-y)(x+y)(-y)(x+y)x+y23.原式二.(ml)2(m-1)(IrrH)2-11H-1_2二ri-2=m-二n-l
10、In-In-ln-lm-l24 .原式=X(x+2)3(X-I)(x+2)=42-3-2-x+2八(x-1)(x+2)(x-1)(x+2)(x-1)(x+2)(X-I)(x+2)二1一一二，；X的取值范围是x-2且xl的实数.(X-I)(x+2)x+225 .原式X1.Mq.n-mn-r26 .1222=12-2(11H3)2(In-3)In2_3m11H3(IrrI3)(m-3)(113)(m-3)(rr3)(In-3)_12-2(rH-3)+2(In-3)-12-2n-6+2n-6_q(11H-3)(In-3)(11H-3)(m-3)27 .原式二2y一y-2xJHX-y2x=匚？二2-y
11、22-y22-y2x2-y2(x+G一丫)x+v28 .a+9b_a+3b=a+9b-(a+3b)二6b二23ab3ab3ab3aba29 原式二(a-b)+(a-c)+(b-c)+(b-a)+(c-a)+(c-b)(a-b)(a-c)(b-c)(b-a)(c-a)(c-b)=1+1+1+1+1+1=O.a-cabb-ab-cc-bc-a30 .原式二，、54+5(x+3)(-2)(x+3)(-4)(-2)(x-4)(2)-+.+=1+1+,+1X(x+l)(x+l)(x+2)(x+2005)(x+2006)xx+1x+1x+2x+2005x+200632b2a+c_bc_b2a+c-b+c-
12、b2a-b+2c2a-2b+2c=_2a-b+cba-cb-a-ca-b+cb-a-cb-a-cb-a-cb-a-c332a2+3a+2_a?-a_5_3a2-4a-52a2-8a+5a+1a+2a-2+a-3二(2a+l)+，-(a-3)(3a+2)+,+(2a-2)a+1a+2a-2a-3=(2a+l)-(a-3)-(3a+2)+(2a-2)+(，-，+，-，)a+1a+2a-2a-334 .原式二(x+y)2_(x-y)2二X+y_1.%+y-+y=2y=2xy(x+y)xy(x-y)xyxyxyxyx35 .原式=xy_!f二(了)-y,_2(x：+，2)2(x+y)(xy)(x-y)
13、2(x+y)(x-y)2(x+y)(xy)x+2y_y-1_y二x+2y-y1.y=+_1一21一21一21一21一一IxIxIxIxIxIx37.原式二要4+/-yX-3y3x-4y_3y-2_22_22-2XyXyXy38.原式二3x(X-I)4.62_(x+5)(X-I)X2(x1)X2(x-1)X2(X-I)39.(x+2)(x+1)(x+2)(-l)(l+x)(l-)40 .原式=1+ll+工+，=2+_J_+，(I-X)(l+x)(1-x)(l+x)+2+4(1-)(l+x)+2+乂441 .设22+3x=y,则原式二，y-1y+1y342 .原式二(a+1)2-a+2=a+l-a
14、+2=3.a+143 .原式二。1.T_x-二零=x+y(x+y)(X-y)(x+y)kx-yJ(x+y)-y)x-y2244 .原式二y+X=y_X=y_X,X(x-y)y(y-x)x(x-y)y(x-y)Xy(X-y)Xy(X-y)45.y.IX=-2_2-2-乂2二(出)(y-)_.+yx2-xyyxx(-y)x(x-y)x(xy)x(-y)x462xy=2xyx(-y)+x(x+y)_2xy+x2-xy+x2+xy=2xy+2x22_y2+2-y22-y2(x-y)(x+y)47 J式二2a_bc_2b-ca2c-a-b、(a-b)(a-c)(b-c)(a-b)+(a-c)(b-c)=
15、，+，-，-，+，+，=Oa-ca-ba-bcbc-bc-a48 .原式=2a-a-l+a+l=2a.49原式二a+(3a+l)-(2a+3)=a+3a+l-2a3=2(a1l)=2*、a2-1a2-1a2-1al50.原式二J-3x+5=1.1.(3x+5)=2-6=一工x+3(x+3)(-l)(x+3)(-l)(x+3)(X-I)-l51.原式二4X-83x+612二7x-14=7(x+2)(X-2)(x+2)(X-2)(x+2)(x-2)(x+2)(x-2)x+252.原式n-2xa(a+3)=a+(a+l)-(a+3)_2a(a+l)(a-1)a+1a+1a+153.原式:2b+2a_
16、2a+b=2b+2a-(2a+b)-2b+2a-2ab.b=12ab2ab2ab2ab2ab2ab2a54.原式二()+(X-Z);(y-x)+G1.Z)十(Z-,x)+(z-y)(-y)(X-Z)(y-x)(y-z)(z-x)(z-y)二1+1+1+1+1+1=1-.1+1-1+1-,1=o+o+o=oX一zX-yy-zy-xz-yz-xx-zx-zx-yxyy-Zyz55 .原式二1+2(x+1)=)+1)、二1(+l)2(+l)256 .(1)原式二1-1+工-1+工-工工1一工二工；2237888(2)原式二工-J+1_-1_=1-1=？009-Xx+1x+2008x+2009xx+2009x(x+2009)57. 原式二Xf2)一工二q(x+2)(-2)x-2x-2x-258. (1)A(2)不正确，不能去分母(3)原式二59. (1),1、二一，；n(n+l)nn+1(2) 1-1=11+1-n=n+1-n=:nn+1n(n+1)n(n+1)n(n+1)n(n+1)(3) 11+1+1=1-1+-_1+_1-l+1-1=1-1=2011T22342011201222334201120122012201260. 原,式=1+1+234+.+2r_1三2+2+4+2“_11.X+1+xxa1x1+x1+x1+xxa
