分式加减法专项练习60题(有答案)ok之欧阳歌谷创编

分式加减法专项练习60题（有答案）欧阳歌谷(2021.02.01)1・啖耳j+(a-1)+陵+aa+13,七扯&-1.X2-1 71+2.a+1a2-16 . 1_ 3 .s-3s(i-3)7 .工危.aa8 .上.—.a+la+16yue289 . 2灯上.J--田后Fbb.a2-b2"bSw_1.m2-4舟"2武士—正二J-4 x2+4x+41 ।55m2-m2m2-2Al-a.欧阳歌谷创编 欧阳歌谷创编 2021年2月1欧阳歌谷创编 欧阳歌谷创编 2021年2月1a-1-2a+l(x-1)(k+2)(x-1)(k+2)19.己2+寸b+b2—b*+：ab+b220一1,1a3-b3b2-2ab-Fb2a2-b2a-1aUa2-1+2+2.-93-itirrl-327.2E+y-2工.28./9b_a+3bx2_y2y£_x2x2_y2 跖卜3ab29.（式中a,b,c两两不相等）：2a-b-c2b-c-a2c-a-b

a2_ab_ac+bcb2_ab_bc+acc2_ac_bc+ab1.("2005)(X-F2006)37.计算:39.计算化简:38.W.—36.计算：^^1一二一一40.计算：_X+1+2+T1zuoguo47.2:广十3k+12x-十3K十三o_a+2a+1-(a-2).55.化简:52.计算：1-口X+3a. 53,计算：aa2-111_2a+b.ab2ab54一化简法-厂工। %-宜-? ।如-父-yy2-sy-zz+yzy2-sy-yz+szz2_kz_yz+sy56．先观察下列等式，然后用你发现的规律解答下列问题：TOC\o"1-5"\h\z由1 11「 1 11「 1 11」, ,lX2-2-l 22X3-6-233X4-12-34(1)计算一1+L+1+1+L+L+1= (n1X22X33X44X55X66XT7XS 为正整数)；(2)化简：—1_H 1 d1 +…+ 1 .k(k+1) (其+1)Cx+2) (k+2)(i+3) (x+200S)(k+2009)957.化简：，电一工. 60,求和x2-4 -4己力…+舟・58．请你阅读下列计算过程，再回答所提出的问题：题目计算：1_ 6a+3 9-a2解：原式一— § (A)a+3 (a+3)(a-3)二53一6 (B)(a+3)(a-3) (a+3)(a-3)=a-3-6(C)=a-9(D)(1)上述计算过程中，从哪一步开始出现错误： ．(2)从B到C是否正确，若不正确，错误的原因是 ．(3)请你把正确解答过程写下来.59.观察下面的变形规律：，=1-工，=_1-工；，=_1-1X2 2 2X32 3 3X43会…解答下面的问题：(1)若n为正整数，请你猜想—1—=；n(n-Fl)(2)证明你猜想的结论；(3)求和：，+，+，+...+ 1 1X22X33X4 2011X2012参考答案：.原式=a_1+=£2_^+]=1+1=2.a-ba-ba-b.原式=@2-a+a(a+1'J=a2-a+a=a2.a+14.原式= -1= 二2 =_JL(工+1) (K-1)X-1 (k+1) (K-1) k+15.原式=，+ Z = 不_ =1.a+1(a+1)(a-1) (a+1)(a-1)a-1.原式= 三 - / =—匚2—=1.k(y-3)x(k-3)k(工-3)x7 .工_^=1±2=3.aaaa8 .原式=/一1=(升1)(51)二a-1.a+1 a+19.原式= 2个+。心r)=(k+/)(k-了) (x+y)(s-y)2sy+J-咫_ ，(工+刊_工(k-y)(肝y)-(k-y)(肝v)-z-y.r-"+h=小-b)+h=a+b="I社之一b之 a+b(a+b) (a-b) a+ba4-b a+b a+b.原式二21n - 卬-2 = =1(nri-2)(id-2)(irrF2)(ro_2) (mi-2)(ro-2)皿-2.原式二「[工-2)一(D(k+2)二工一一二1(k-2)(k+2) (x+2)* k+2 i+2k+2.原式= 2(/1) +in」—5)二八一3/2二2m(in_1)(irrl-1)2m(in_1)(irH)2m(in_1)(irH)(in-1)(卬-2)2m(in_1)(irH)TOC\o"1-5"\h\z= 522m(mH).原式二屋+(—)(L」二屋十1一f=1.1+a 1+a 1+a 1+a. L1 -a2+a二=2m(HI)=[-a=1—三a2-2a+la£-1(a-l)2 (a-l)(a+1)a-1a-1a-1-1..⑴原式==-2(舟3)二-25-3)二一2 ;(irr^S)(in_3)CnH-3)(id_3) (nrl-3). 1. 4 = 升2 _ 4a-2 (a+2)(a_2) (a+2)(a-2) (a+2)(a-2)/2-4(a+2)(a-2)二a-2=1.(a+2)(a-2) a+2原式=1-原式= .2>.b+b* (a-b)Ca，ah十b2)f •(a+b)』b)=1_ = =L-b(己一b)2b(a+b)a-b(a-b)a-b11L—&=a+mm=口=0a-1a+1屋-1 (a-1)(a+l)(a+1)(a-1)

1m1m-.原式=工但)_ 3 _(耳一1)〔肝公二(k-1)Ck+2) (k-1)(k+2)Ck_1)[x+2)k2+2k-3-J-k+2(s-1)(k+2)= 3 =_X；x的取值范围是x^-2且xR1的实数(k-1)(k+2) k+2.原式二2卬一口一也0二m.n_w n_ir. 12,_S_2=1tl2—g3-mirH-312 -2(m+3) 25-3)(irrl-3)Cm-3)+(时3)(m_3)~+(时3)[皿一3)」2-2(说3)+2(m-3)=12-如-&+瓦-6=0(irH-3)(id-3) (时3)(m-3).原式二⑷文一可-2_„2 2_„2如二阳一厂2"二K2-y2J-$(s-Hy)(k-y)x+y.什弗一旬.二a+9b-〔升3b)6b2.3abSabSab_3ab-a.原式=(m-b)+(a-G+(b-G+(b-a)+(C+(bb)(a_b)(a_c)(b_c)(b_a)(c_a)(g_b)=1+1+1+1+1+1=0.a-ca-bb-□b_cc_bc-□.原式=5, + 2工-5 -7fTQ(x+3)(k-2) (k+3)(k-4) (k-2)(x-4)二5无(l4)+(以一5)(l2)-(TlLO)G+3)=(z+3)(x-2)(k-4)-40k+40(k+3)(x-2)Ck-4)31.31.(2) 1H + +...+ 1 =1-_L+_Lk(k+1) (s+1)(，+2) (k+2005)(k+2006)xk+1k+1-1+…+L一Lk+2 k+2005 z+2006二2-1= 20OS.kk+2006k(i+2006)匕+方+，_b-c=a-b+cb_a_cb_a_cb—b+c_一七并―b+2c_2a—2b+2c=-2a-b-l-cb_a._gb_a_cb_a_cb_a_c2屋+而+2一相一耳一5一3色2-为一5二2一.十5a+l a+2 a_2a-3=(2a+l)+1-(a-3)-_L_(3a+2)+1+(2a-2)-a+1 a+2 a-2a-3=[(2a+l)-(a-3)-(3a+2)+(2a-2)]+(1-1+1a+1 a+2a-2-^—)a-3=1.1+1-1二1 a+1 a+2a-2a-3(a+1)(a+2)Ca_2)(a-3)= F+4 (a+l)(a+2)(a-2)(a-3)34.，原式二b+F)- 2=x+y一耳一y="y—/y=2y=2sy(x+y)sy(s_y)xyxyxy 工35.原式39.原式二40.原式)(1+X2)(1+X2) 1十工（1十产）一（1+J）1-2+，

2+，

y+ly+341.设2x2+3x=y,则原式二1y-1=MD(v+3]-2(y-1)(y+3)+Cy-1)[y+1)=(y-1)(y+1)(y+3)(y-1)(y+1)Cy+3)： 3C2i2+3s-1)(2x2+3i+1)(2x2+3i+3)42.原式二1a+1)?-a+2=a+1-a+2=3*a+143.原式44.原式)+(g-bja-c1(a-b)(1+11+1(c-a)(c-b)(k-y)(s+y)47.原式二 ：(a-b)((a-b)+(a-c)+,(b-c)(a-b)a-ca-ba_bc_bc_b=048.原式=2@-a-1+a+1=2a.49.原式心工②+3)=/3员+1-%-3=2Ca-D=2a2-la2-1 什150.原式51.原式52. 原式=1-1宗&〈已+3) =1-m+S=(a+1)-(色+3)=一a(a+1)(a-1) a+1 a+1w53. 原式=为+2a-2a+b=2b+2a-(2色+b)=2b+2：a-2色-b=b=12ab2ab2ab 2ab 2ab2ab2a54.原式二一一举)+D+G+(广外+ +包-『)(x_y)(i_z) (y_k)(y~z) (z-x)(z-y)=l+」+l+l+」+L=L-L+1-1+1-x-lk_yy_ey~xz-yz-x篁一工篁一工k_yk_yy-e1=0+0+0=0y~e55.原式一晚—-(k")=S+l)Li(s+1)2Cx+1)256.(1)原式=1T+D…+JLT=1T=』；223 7SSS(2)原式=1-1+…+1 - 1=1- 1=加09工k+1 k+2008k+2009工k+2009k〔升2009)57.原式二i(耳+2) 一2=上一==1(x+2)(k-2)x_2篁-2l258.(1)A(2)不正确，不能去分母(3)原式=[j8 = l3 , § =a+3(a+3)(a-3) (a+M)(a-3) (a+3)(a-3)m-3+6a-F3(a+3)Ca_3) Ca+3)(a_3)a_359. (1)—1―=!」；n(n+1)nn+1(2)=一〉二门+1一■二