分式加减法专项练习60题(有答案)

分式加减法专项练习60题（有答案）

1.

2,

2.a(a-1)+-5-^

a+1

3.

4.1

x2-lx-l

5

02

a+1a-1

6.13

x-3x(x-3)

7.

8.亡」.

a+1a+1

6yue28

9.上。+工

乂2—2x+y

2

10.a-ab+工.

a2-b2m

2m_1.

m2-4"2.

x。-2x_x2+x2

x2-4X2+4X+4

1in-5

m221n2-2

2

15a-1_a+a

a2-2a+la2-1

2+9X1.2—9

16.(1：'^--^-:⑵x

ID2-9m-3X2+3Xx2+6X+9

2.2

1_4mn

17.18.

2

a-2a-4l2n1rl2_4im+4n2

19a2+ab+b：_b"-ab+b220

a3-b3b2-2ab+b2a2-b2-£舄一帚

21.口4x22.-上

x+1X2-1x2-y2x-y

9

in+2mH_23

23.24.-1,

ro2-lm-1x-1(x-1)(x+2)

2

31.(1)」-x+y；

x+y

x(x+1)”(x+l)(x+2)’•.(x+2005)(x+2006)

b*2a+c_b-c

a_b+cb_a-cb-a-c

33.化简分式:量也"g一a?-a-5_3a2-4a-5叶202-8a+5

a+1a+2a-2a-3

22

x2+2xy+y2x2-2xy+y2x-y_

34.35.计算:

2222

xy+xyxy-xy2x+2yx2-y2,

36.计算：以与+与、--x+2y3y-x3x-4y

37.计算：一+

1-X2X2-11-X27-Z~~22_22_2

xyyxy

38--6_x+539.计算化简：——十2

222

.x1-xx2X+3X+2x+x-21-x

40.计算：，_+，+，_+」_41.计算121

24222

1-x1+xi+xi+x2X+3X-12x+3X+12X+3X+3

2

43.化简：,+2y

42.计算：a+2a+l-（a-2）.

a+1x+yx2-y2,

2

44.---i_—45.计算：。_

x2-xyy2-xyx2-xyyx

zuoguo

46.+工-上.55.4匕简：/11g.

22

x-yx+yy-XJ+2x+lx+1

2a-b_c2b_c-a2c-a-b

(a-b)(a-c)+(b-c)~~(b-a)+(c-a)""(c-b)

a3a+l2a+3

48.2a-(a+1)+^—2_1_2_+7TT2-

a-111

50.计算：，-户+5

2「计算：嘘一望；

x+3x+2x-35Ur

a-1

52.计算：1-53.计算：工二-冽也

aa2-1ab2ab

2x_y_z2y_x_z2z_x-y

54.化简

-99+o

xxy-xz+yz寸—xy-yz+xzzxz-yz+xy

56.先观察下列等式，然后用你发现的规律解答下列问题:

由，』」一___L_1-U

1X2-2-122X3"6"233X4-12"34

(1)计算」二(n为正整数)；

1X22X33X44X55X66X77X8

(2)化简：---~：-4-~：---------：—----：—4-~：----：—-----：—+••,+—：----------：—----------：—

x(x+1)(x+1)(x+2)(x+2)(x+3)(x+2008)(x+2009)

57.化简：x：+2x__g_n

60.求和1.2,4,.2

2-24

x-4x21+x1+x1+x1+x1

58.请你阅读下列计算过程，再回答所提出的问题：题目计算:16

a+39-a2

解：原式=,

6(A)

a+3(a+3)(a-3)

a一3

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)讲你把正确解答过程写下来.

1

59.观察下面的变形规律：1=1-工;1二工-。;=1-1

1X222X3233X434

解答下面的问题：

(1)若n为正整数，请你猜想，1、二______________;

n(n+1)

(2)证明你猜想的结论：

(3)求和:——+_L_+_L_+--•+--------1----------.

1X22X33X42011X2012

参考答案:

原式二一-±+『=+1=1+1=2.

1.

a-ba-ba-b

P；v,2,a(a+1)_2工_2

2.原式-a-a+----------a-a+a-a.

a+1

b2.,"+相卡二&2

3.

a-b&a-ba-b

4.原式二一2x_1二x_l二]

(x+1)(X-1)X-1(x+1)(X-1)x+1

原式二，_+___________2=a-]+2=]

5.

a+1(a+1)(a-1)(a+1)(a-1)a-1

6.原式二--------------------------------=—3二工.

x(x-3)x(x-3)x(x-3)x

7.毕屿工

aaaa

8.原式二(a+1)

a+1a+1

2xy,x(x-y)=2xyFx」-xy_x(x+y)x

(x+y)(x-y)(x+y)(x-y)(x-y)(x+y)(x-y)(x+y)x-y

10a_ab4b=a(a-b)与b二a+b二a+坛1

22

a-ba+b(a+b)(a-b)a+ba+ba+ba+b

m2二M2二1

11.原式二.2m

(M2)(m-2)(irr+2)(in-2)(irrl-2)(m-2)m_2

二x(x-2)_(x-1)(x+2)_x_x-2]

(x-2)(x+2)(x+2)2x+2x+2x+2

13-原式二茄嵩且焉in(in-5)二11)2-3/2_(in-1)(ID-2)

2m(in-1)(m+1)2m(in-1)(m+1)2in(in-1)(m+1)

m-2

2ro(m+1)

14.原一二二+(1+a)(—a)=”+112二,

1+a1+a1+a1+a

a-1_a2+a__a(a+1)=1_a二1_j_1

a2-2a+la2-1(a-1)2(&-1)(a+1)a-1a-la-l

(1)原式二/2:2(/3)-2(m-3j

16.2

(nrt-3)(in-3)(m+3)(in-3)(m+3)

⑵原管忧"7+；二"氏上今有1=2

17.14a+24a+2-4

a-2(a+2)(a_2)(a+2)(a-2)(a+2)(a-2)(a+2)(a-2)

a一21

(a+2)(a-2)a+2

m-n(in-2n)2_qID_2n_ro+n-(m-2n)_irrl-n-m+2n_3n

18.原式二1--1------------------------------------

m-2n(irrt-n)(in-n)m+nin+nm+nnH-n

a2+ab+b2b2.(a+b)(a-b)二1

19.原式二，bl-b

(a-b)(a2+ab+b2)(a-b)2b(a+b)a-b(a_b)a-b

11_2a_a+l+a-1-2a=_______0

2--

a"■1a+1a-1(a1)(a+1)(a+1)(a1)

2

(x-1)x4x=(x+1)2=x+1

(x+1)(X-1)(x+1)(X-1)(x+1)(X-1)X-1

2xy?(x+y)=y(x-y)二y

22.原式二

(x-y)(x+y)(x-y)(x+y)(x-y)(x+y)x+y

23.原式二,(吁)，2、-2二/1_2二时1一2二口J.

(in-1)(nr+l)in_1m_1in_1in-1in-1

24原式二x(x+2)_________3________(x-1)(x+2)=/+2x-3-x2-x+Z

,，'"(x-1)(x+2)(x-1)(x+2)(x-1)(x+2)~~(x-1)(x+2)

———J——L=，；X的取值范围是xW-2且X丰1的实数.

(X-1)(x+2)x+2

25.原式/…飞二工

n-IDn-n

261222._______12______-2(nH~3)2(m-3)

--

1n2-9+3—m+/3一(irH-3)(m-3)+(m+3)~(m3)*("3)"""(m3)

_12-2(irH-3)+23)122m-6+2m6_Q

(ITH-3)(m-3)(irrl-3)(m-3)

27.原式二21一y一2x*一'一"______

x2-yzx2-yzx2-yzx2-y2但+y)(x-y)x+y

28a+9b_a+3b=a+9b-(a+3b)6b2

3ab3ab3ab3aba

29原式=(a-b)+(a-c)q(b-c)+(b-a)二(c-a)+(c-b)

(a-b)(a-c)(b_c)(b_a)(c-a)(c-b)

，+，+，+，+，+，二0

a-ca_bb_ab_cc_bc_s

2x-5_7x70

30.原、式二•

(x+3)(x-2)(x+3)(x-4)一(x-2)(x-4)

5x(x-4)+(2x-5)(x-2)(7x-10)(x+3)-40x+40

(x+3)(x-2)(x-4)(x+3)(x-2)(x-4)

29222

⑴上一X+y,二工

31.

x+yx+yx+yx+y

⑵xJl),1.+•・•+.1-_1-14.1!+•・•+.11

(x+1)(x+2)(x+2005)(x+2006)Xx+1x+1x«2x12005K12006

二」1-2006

7x+2006x(x+2006)

b+2a+cb-cb2a+c-b+c-b2a-b+2c2a-2b+2c.2

32.

a-b+cb-a-cb-a-ca-b+cb_a_cb_a_cb_a_cb_a-c

o2a-53a4a-52a2-8a+5

33.2a+3a+2a一

a+1a-2+a-3

=(2a+1)+‘-(a-3)--L-(3a+2)+，_+(2a-2)--L.

a+1a+2a_2a_3

=[(2a+1)-(a-3)-(3a+2)+(2a-2)]+(——-——+―------)

a+1a+2a-2a-3

11

a+1a+2a-2a-3(a+1)(a+2)(a_2)(a-3)

-8a+4

(a+1)(a+2)(a-2)(a-3)

(x+y)2_(x-y)工Iy_x-yx+y-x+y2y2

34.原式工

xy(x+y)xy(x-y)xyxyxyxyx

x2+y2(x-y)(x-y)2(x2+y2)

35.原式二

2(x+y)(x+y)(x-y)2(x+y)(x-y)2(x+y)(x-y)

_x2-2xy+y2-2x2-2y2

2(x+y)(x-y)2(x-y)

36

—yx+2y-y+l-yX«11

1丫21-丫2i--

37.原式二等勺x-3y3x_4y_3y-x

X2-22_,22_„2

xyyxyxy

2

3x(x-1)+6x(x+5)(x-1)

38.原式二

x2(x-1)x2(x-1)x2(x-1)

3x(x-1)+6x2-(x+5)(x1)8x27x+5

X2(x-1)X2(x-1)

39.原式二------------------+--------------------+--------------------

(x+2)(x+1)(x+2)(x-1)(1+x)(1-x)

_x(x-1)x(x+1)2(x+2)

-----------------------------------------------------------十-----------------------------------------------------------------------------------------------------------------------

(x+2)(x+1)(x-1)(x+2)(x+1)(x-1)(x+2)(x+1)(x-l)

:x2-x+x」+x-2x_4=_____2X2-2X-4=2(x-2)(x+1)=2x~4

*2*2

(x+2)(x-1)(x+2)(x+1)(x-1)(x+2)(x+1)(x-1)x+x-2

40,原式二___________________+_______111_____+_g_+4二_________?_________+_2_+^_

22

(1-x)(1+x)(1-x)(1+x)|+x1+J(1-x)(1+x)i+x1+x4

-2(")―2(1-x2),4.4一4

(1-x2)(1+x2)(1-x2)(1+x2)1+x4*1-X41+x4

44

4(1+x),4(HX)8

(1-x4)(1+x4)(1-x4)(1+x4)1-x8,

41.设2x2+3x=y,贝I原-2+-L

y-1y+1y+3

J〉l)(y+3)-2(y-l)(y+3)+(y-l)(y+1)=*

(y-1)(y+1)(y+3)(y-1)(y+1)(jH-3)

=__________________8__________________

(2X2+3X-1)(2X2+3X+1)(2X2+3X+3)

42.原式二(a+1)2_a+2=a+1-a+2=3.

a+1

43.，原式-1+2y-x-y+2y_x+y_1.

x+y(x+y)(x-y)(x+y)(x-y)(x+y)(x-y)x-y

22

44.原式二_____—__________________=_____X.___—_________=____Z_____—_____,

x(x-y)y(y_x)x(x-y)y(x-y)xy(x-y)xy(x-y)

二，I2二一(x+y)(x-y)=_x+y

xy(x'y)xy(x-y)xy

45y2|x二丫2_F二y2一乂2二(>x)(y_x)._西

x2-xyy-xx(x-y)x(x-y)x(x-y)x(x-y)x

462xyx_x_2xy4~x(x-y)+x(x+y)_2xy+J-xy+x2+xy=2xK2,2

■J_y2+而x2-y2x2_y2(x-y)(x+y)

=2x(x+y)=2x

(x-y)(x+y)x-y

47厝式=2a-b-c_2b-c-a2c-a-b

'(a~b)(a-c)(b-c)(a-b)+(a-c)"""(b'c)

-__-

_(ab)+(ac)_(b-c)+(ba)+(c-a)+(cb)

(a-b)(a-c)(b-c)(a_b)(c_a)(c-b)'

a-ca-ba_bc_bc_bc_a

48.原式二2a-a-1+a+1=2a.

AQ盾少_a+(3a+l)-(2a+3)_a+3a+l12a-3_2(a_1)_2

*222

a-1a-1a-1a+1

50原式二_3x+5=x-1-(3x+5)=-2x-6二_2

7^3(X+3)(X-1)(x+3)(x-l)-(x+3)(x-1)7Tl

51.原式:4X—83X+6_12;7x74二工

(x+2)(x-2)「(x+2)(x-2)(x+2)(x-2)(x+2)(x-2)x+2

52原式二1-a-l)<a(a