Upload
ebookcraze
View
242
Download
0
Embed Size (px)
Citation preview
8/13/2019 3 6 Partial Fractions
1/12
^orteoc Iromtejks
=.9
Ektrjhumtejk
Et es jitdk bdcpiuc tj `rdoa hjwk o mjgpcemotdh ocfd`roem iromtejk ektj o sug ji segpcdr iromtejks. Ijr
dxogpcd et mok `d sbjwk tbot 8x+ 6
x0 + =x+ 0bos tbd sogd vocud os
?
x+ 0+
=
x+ ?ijr oky vocud jix.
Vd soy tbot
8x+ 6
x0 + =x+ 0 es ehdktemoccy dquoc tj
?
x+ 0+
=
x+ ?
okh tbot tbd porteoc iromtejks ji
8x+ 6
x0 + =x+ 0 ord
?
x+ 0 okh
=
x+ ? .
Xbd o`ecety tj dxprdss o iromtejk os ets porteoc iromtejks es portemucorcy usdiuc ek tbd stuhy ji Copcomdtroksijrgs, \-troksijrgs, Mjktrjc Xbdjry okh Ektdfrotejk. Ek tbes ]dmtejk wd dxpcoek bjw porteociromtejks ord ijukh.
^rdrdquesetds
@dijrd stortekf tbes ]dmtejk yju sbjuch . . .
`d iogeceor wetb ohhetejk, su`tromtejk,guctepcemotejk okh hevesejk ji ocfd`roemiromtejks
Cdorkekf Jutmjgds
Jk mjgpcdtejk yju sbjuch `d o`cd tj . . .
hestekfuesb `dtwddk prjpdr okh egprjpdriromtejks
dxprdss ok ocfd`roem iromtejk os tbd sug ji ets
porteoc iromtejks
9> BDCG (0>>4) 7 O(>) +@(0 + =)
= 7 @
sj tbot tbd mjkstokt @ gust dquoc =. Xbd mjkstokt O mok `d ijukh detbdr `y su`stetutekf sjgdjtbdr vocud ijr x jr octdrkotevdcy `y dquotekf mjdmedkts.
J`sdrvd tbot, `y rdorrokfekf tbd refbt-bokh sehd, Dquotejk (*) mok `d wrettdk os
6x+ ?> 7 (O+ 0@)x+ (O+ =@)
Mjgporekf tbd mjdmedkts ji x jk `jtb sehds wd sdd tbot 6 7 O+ 0@. Vd ocrdohy akjw@ 7 =
okh sj
6 7 O+ 0(=)
7 O+ 9
irjg wbemb O7 ?. Vd mok tbdrdijrd wretd
6x+ ?>
0x0 + 4x+ =7
?
0x+ =+
=
x+ ?
Vd bovd summddhdh ek dxprdssekf tbd fevdk iromtejk os tbd sug ji ets porteoc iromtejks. Xbd rdsuctmok ocwoys `d mbdmadh `y ohhekf tbd iromtejks jk tbd refbt.
BDCG (0>>4)+
M
x ?
Ierst guctepcy `jtb sehds `y (x0 +x+ ?>)(x ?))
Dvocuotd M`y cdttekf x7 ?)+
?
=(x ?)
92 BDCG (0>>4)>4) es o mjkstokt, O soy,
o pjcykjgeoc ji hdfrdd ? bos tbd ijrg Ox+@,
o pjcykjgeoc ji hdfrdd 0 bos tbd ijrg Ox0 +@x+M,
okh sj jk.
Ei, ijr dxogpcd, tbd egprjpdr iromtejk es sumb tbot tbd kugdrotjr bos hdfrdd 4 okh tbd hdkjgekotjrbos hdfrdd =, tbdk k h7 0, okh wd kddh tj ohh o pjcykjgeoc ji tbd ijrg Ox0 +@x+M.
Ady ^jekt ?6
Ei o iromtejk es egprjpdr ok ohhetejkoc tdrg es ekmcuhdh toaekf tbd ijrg ji o pjcykjgeoc ji hdfrddk h, wbdrd k es tbd hdfrdd ji tbd kugdrotjr okh h es tbd hdfrdd ji tbd hdkjgekotjr.
6> BDCG (0>>4)x0
08x 05(x+ 0)0(x =)
, (i) 8x4
+ 2x8
+ 0=x=
+ 06x0
+ 04x+ 5(x0 +x+ ?)(0x+ ?)
Okswdrs
(o) ? + ?
x+ 0 (`) = +
0
x =, (m) ? + x+
?
x+ ? (h) 0x+ = +
?
x+ 0,
(d) ?
(x+ 0)0+
?
x+ 0+
?
x =+ =x0 +x+ 0, (i) 0x0 +x+ 6 +
?
0x+ ?+
?
x0 +x+ ?
BDCG (0>>4)