分式知识点及典型例题

0 0 0

0B0 0B0

0

bcdaaac

cb?d 0,c0;

dac

bd

ac

.同分母加减法则：P-上三aaa

:b bcda

a

cacac

:b?d bdb

acaca

4.

5.

;am an=am+n;aman=amn

:(ab)m=ambn,(am)n=amn

1

:a-p=1a0=1

ap

: (a+b)(a-b)=a2-b2;(ab)2=a

22ab+b2

AB

B

B0

A0A0 0

B0B0 0

B0B0

1 A=B -1 A+B=0

0

AA?CAAC

ABC C0

BB?CBBC

a?ca?c

bdb?d

acada?d

bdbcb?c

n

aban bn

acadbc

bdbd

x0<x<1 a10n1a10a n

mnmn

aaa

abnan1bn

mmn

aa

amanamn a0

aan

nnbb

an

n

na

a01

nn= 0

0.000000125=1.2510-7

70

x x>10 a10n1a10 a n

n=

120000000=1.2108

1

3（x1）22

x,12xy,ab,xy

ab

xyxy—xy

1 x42 3x3

X4 x2

2

2

2x

6x

33

0.

x1

x3

Ix|2

x24

x2x3

x5x6

41

8x

5x

3 x

x3

#

2

1

6|x|3

3x

(x1)21

(3)

5|x1|

x4

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x26x5

|xx|12

2x2x2x530

12

xy23——

11

0.2a0.03b

0.04ab

34xy

2

5 |xy1|(2x

#

)2 0 4x12y

115 2x3xy2y

xyx2xyy

xy3xy

xy

4 x1x2 x2x12

#

0.03x0.2y

0.08x0.5y

0.4a3b

5

iaib

410

12

.

4x2

xa22ab26b10

x21

113 2a3ab2b

abbaba

32aa5bb

x1|x||x1|

|x2x2|

x

#

16xgy

20xy

mn xx6

2ab,3a2c,

5b2c

a,bab2b2a

2x2x,12xx2,x2x2

2,

2a

22

#

22

1 (acb)3(cab)2(bac)4

caba

2 3a3(x2

(

y2)

yx2

( )2

yx

m2nn 2m

nmmnnm

2

(4)-1;

2x

3

4x

4

1x

z

x8

1

(x1)(x1)

1

(x1)(x3)

1

(x3)(x5)

8[(x41)(11)x]44x

2 xy

#

23

xy2yz3xz

22xy 2

3 a23a10 (a212)(a1)

aa

5 13x M xN1 M,N

x21 x1

2a5al2a3 be2ab

2(a1)获百询) 2日ba

abca2b3cb2cabcbcacab 2b2ab

(4)ab

x1

1

(x2)(x3)

21

(x1)(x3)(x1)(x2)

211 aa2 a0.

a1

a2a22a21

22

x:y2:3 (xy)[(xxy

xy

yx)( y)3]

5x4 A2B1

AB

(x1)(2x1)

2 xx1

#

1 x2 x2 2 x4 x4

399a805

a2

1 (a2)3(bc1)3

2 (3x3y2z1) (5xy2z3)

35

4[(xy)3(x

y)22]22(xy)

3 2)3. 32232231 (3103)(8.2102)2 2

1(1315)(51)2|13|(13)0

2007 42008

(0.25) 4

(4103)2(210

132223(3mn)(mn)

3 (a2b)22222(2ab2)2

3 (ab3)232(3ab)

222

[4(xy)2(xy)2]2[2(xy)1(x

y)]2

x2

5x10

x2

111

xy2

zx4

x1

z3

x1

4x4

(1)

(2)

(3)

x3

2

x1

x1

x1

xx76

x2

5x

1；(4)x3-

x9x10x6

x8x9x5

x5

4x

x23 xm3

2xa

"x2"

2a

a2a4.

6 x xac（cd0）bxd

1a,b,c,d 2cd0.

1

4 k x xx32(x1)k(x2)1

x1x1

2x

12x

x3

2x

x2

3

x2

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3

XX

x2

5x4

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1

x1

11

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1

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x

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5

x 2xa

#

a a

1 2

x1 x21

3

x818

x77x

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#

x2 17

1a1b

axbx

(ab)

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4x

#

1111

x2x5x3x4

xx12

x1

x21

xx1

3 kx4

3 x x12xk2 2

A1 B2 C3 D4

2

1.

1 k5

1xxxx2

xk211

x+y,,

ab

32xy5a

B2C

4xy

x

a

b

B

2

ab

x3

5

b

x3,5

xa

2

1

b

4ab

(xmy)

1x___

2x

x2

2 X y

2x

x1

x1

2x1

3 x x

24

2x

x1

x2

3x8

x3

x3

A.

X3

B.

D.1

c.X

D.X21

2XXx21

X0

CX0

DX

2X2y3y

Xy

Xa

3X

2y

3X

2y2

C

2y

D

3. Xy

aaby

6x(yz)

3(yz)2yz

3a

5xy

a21

a24

10axy(a0)

x2x3=x23x

0.5x0.2

0.3y1

bm

abB=0

ab

ab1b1

ac1c1

xy

xy

xy

12

22

ab+b2(2)2a2-2ab

(3)-x2+9

(4)2a3-382a2+8a

x26x9

2x^4

22x28x8=

12xy

2 (2)

9x

ba

b2

(3)

x26x9

a2

(4) a2

b2

ab

16

2m3m 9

4

2x22y25xy

m2

m3

m3

3m

m3

x24x2x

A

6

1

2

8

1

2

3

9

1.

1

13x

x0

2x

1

A

2x12

122

m29m3

6

2

m29

11

11

0

11

6x

5

6x

11

D一

6x

2

2

B

m3

2x

1x2

x1

x21

x1

2

m3

2m9

2m29

x21

x=2

2. 6 x32x1x1

x=

38

x1

x=

2

10

1

-3

-2

223

4 （13）0

3 （3）3

2

2 0.000501=

3 1.2110-5

11

TOC\o"1-5"\h\z

ml x

1 0 m

x44 x

D.3

A.2 B.2 C.3

2

16 3 3 1

12xx

53 x2

12x3x1 2x

13

19 8 9000

7200

5400

20 10 30

2

22

1.5