Fracciones Algebraicas
February 9, 2023 | Author: Anonymous | Category: N/A
Short Description
Download Fracciones Algebraicas...
Description
;.> Jxprjsdghjs `rkccdghkrdks
Jljrcdcdg ;13
;1: _jqujrdidjhtgs nj ckfgréks Jf rjqujrdidjhtg nj jhjrmék
x
K x ? y ?
D
DD
okskf pkrk uhk pjrsghk dhndck jf hüijrg iéhdig nj ckfgréks hjcjskrdks pkrk ikhtjhjr prgcjsgs jsjhcdkfjs nj sgstjhdidjhtg nj fk vdnk, cgig sgh cdrcufkcdóh, rjmufkcdóh nj fk tjipjrkturk cgrpgrkf y rjspdrkcdóh. Nkng jf sjxg, pjsg w (jh bdfgmrkigs), jstkturk e (jh cjhtéijtrgs) y jnkn y (jh kûgs) nj uhk pjrsghk, pgnjigs jstdikr jf rjqujrdidjhtg nj jhjrmék okskf jh ckfgréks uskhng fks `óriufks sdmudjh-
D
DD
tjs, C i yrjspjctdvkijhtj< C e sgh fks ckfgréks hjcjskrdks pkrk iuljrjs ynghnj egiorjs,
y
;1>
>:
Jhcujhtrj fgs vgfüijhjs nj fks cklks D, DD y DDD nj fk `dmurk pkrk jstkofjcjr fk `óriufk nj fk nd`jrjhcdk nj ngs cuogs pkrk jf cksg jspjcdkf x y.
00.:
C e
0::
;3.5w
4.0w
:e
0.5 y
;.4e
>.= y
Njtjridhj fgs rjqujrdidjhtgs nj jhjrmék okskf prdijrg pkrk uhk iuljr nj ?: kûgs nj jnkn quj pjsk :4 bdfgmrkigs, quj idnj ;03 cjhtéijtrgs nj jstkturk y fujmg pkrk uh egiorj nj :: kûgs nj jnkn quj pjsk =: bdfgmrkigs y idnj ;=5 cjhtéijtrgs nj jstkturk.
(o)
Jxpfdquj pgr quä, jh kioks `óriufks, jf cgj`dcdjhtj pkrk y js hjmktdvg pjrg fgs gtrgs cgj`dcdjhtjs sgh pgsdtdvgs.
x
D
7
y
(k)
Jljrcdcdg ;1>
7
C i
DD P x x 3 y y 3
DDD 7
;. ;.>> Jxprjsdghjs `rkccdghkrdks
Zhk jxprjsdóh `rkccdghkrdk js uh cgcdjhtj nj ngs jxprjsdghjs kfmjorkdcks. Cgig cksg jspjcdkf, uhk jxprjsdóh rkcdghkf js uh cgcdjhtj p/q nj ngs pgfdhgidgs p y q. Cgig fk ndvdsdóh jhtrj cjrg hg jstë pjridtdnk, jf ngidhdg nj p/q jstë `grikng pgr tgngs fgs hüijrgs rjkfjs jxcjptg fgs quj ekmkh quj jf njhgidhkngr sjk cjrg. Ngs dfustrkcdghjs sj nkh jh fk tkofk sdmudjhtj.
Jxprjsdghjs rkcdghkfjs Cgcdjhtj 0 x ?
?
x x 3
: x >
4 ? 3 x y > y?
y
3
x
Jf njhgidhkngr js cjrg sd x
y y
3
3
x
Ngidhdg ^gnk x
3
^gnk x y y tkfjs quj y
3
x
>0
CKQÉ^ZFG ; CGHCJQ^GS @ZHNKIJH^KFJS NJ ËFMJO_K
t rkoklg hgs gcupkrjigs nj jxprjsdghjs rkcdghkfjs jh Jh cksd tgng hujstrg trkoklg fks quj tkhtg jf huijrkngr cgig jf njhgidhkngr sgh pgfdhgidgs cgh sófg uhk vkrdkofj. Cgig fks vkrdkofjs nj uhk jxprjsdóh rkcdghkf rjprjsjhtkh hüijrgs rjkfjs, pgnjigs uskr fks prgpdjnknjs nj cgcdjhtjs nj fk Sjccdóh ;.;, sustdtuyjhng fks fjtrks k, o, c, y n cgh pgfdhgidgs. Fk sdmudjhtj prgpdjnkn js nj pkrtdcufkr dipgrtkhcdk, nghnj on 1< kn k on o
n k n o
;
k o
K vjcjs njscrdodigs jstj prgcjsg nj sdipfd`dckcdóh kf njcdr quj uh `kctgr cgiüh nd`jrjhtj nj cjrg jh jf huijrkngr y njhgidhkngr nj uh cgcdjhtj sj pujnj ckhcjfkr. ckhcjfkr. Jh fk prëctdck, pgr fg mjhjrkf igstrkigs jstk ckhcjfkcdóh pgr ijndg nj uhk ndkmghkf sgorj jf `kctgr cgiüh, cgig jh fk sdmudjhtj dfustrkcdóh, nghnj tgngs fgs njhgidhkngrjs sj supghj quj sgh nd`jrjhtjs nj cjrg.
DFZS^_KCDÓH
@kctgrjs cgiuhjs ckhcjfkngs kn on
k
ih
o
hpq
i
pqr
pq
rpv
q v
Zhk jxprjsdóh rkcdghkf sj sdipfd`dck g sj rjnucj k su iéhdik jxprjsdóh , sd jf huijrkngr y njhgidhkngr hg tdjhjh cgig `kctgrjs cgiuhjs pgfdhgidgs nj mrkng pgsdtdvg y hg eky `kctgrjs cgiuhjs jhtjrgs ikygrjs k ;. Qkrk sdipfd`dckr uhk jxprjsdóh rkcdghkf, `kctgrdzkigs huijrkngr y njhgidhkngr jhtrj `kctgrjs prdigs y fujmg, supghdjhng quj fgs `kctgrjs njf njhgidhkngr hg sgh cjrg, ckhcjfkigs `kctgrjs cgiuhjs cgig jh fk dfustrkcdóh sdmudjhtj.
DFZS^_KCDÓH
Jxprjsdghjs rkcdghkfjs sdipfd`dcknks sd x ?
3 x ?
x ?
: x ?
>
? x 3 x ? 0 x ?
x
?
3 x ; x x ? o 3 x ; x x ? x x ? x ? 3 x ?
0 x ?
x
x
?
?
sd x ?3
3 x ? x x ; o
3 x ?? x ; sd x :, x
x x ? 5 x ;0 x x : x ? : x x ? ;0 x x
x ;
? x ; >
; ??
o x > x x >) > ( x x x :) : ( x x x x x > x ( x x :)( x x >)( x x >)
Cgig sj vj jh jf jljipfg sdmudjhtj, cukhng sj sdipfd`dck uh prgnuctg g cgcdjhtj nj jxprjsdghjs rkcdghkfjs, cgh `rjcujhcdk uskigs prgpdjnknjs nj cgcdjhtjs pkrk gotjhjr uhk jxprjsdóh rkcdghkf. K cghtdhukcdóh `kctgrdzkigs jf huijrkngr y njhgidhkngr y ckhcjfkigs `kctgrjs cgiuhjs, cgig edcdigs jh fk dfustrkcdóh prjcjnjhtj.
;.> Jxprjsdghjs `rkccdghkrdks
>=
Qrgnuctgs y cgcdjhtjs nj jxprjsdghjs rkcdghkfjs
JLJIQFG ;
J`jctüj fk gpjrkcdóh dhndcknk y sdipfd`dquj<
(k)
x ?
0 x 4 ? x ?
x ?
;
x ?
(o)
x 3
? x 3
x ?
>
? x ?
3 x
SGFZCDÓH
(k)
x x ? 0 x 4? x ? x x ? ; x x 3
x ? 0 x 4 ? x ? x ? ; x 3
prgpdjnkn nj cgcdjhtjs
;
3)?? ?( x ;) ( x x 3 ? x ; ; x ; x x 3) 3 ( x x ;)( x ;)(
`kctgrdzkr tgngs fgs pgfdhgidgs
sd x 3, x ;
o ? x x 3
(o)
x ? ? x 3
x ? ?
? x
> 3 x
sd x
x ;
x ?
? x 3
o
? x ?
3 x
?
>
x
prgpdjnkn nj cgcdjhtjs
x x ? x x ? x 3 ? x 3 x x ? x x ?
?, x
ckhcjfkr `kctgrjs cgiuhjs
prgpdjnkn nj cgcdjhtjs2 `kctgrdcj tgngs fgs pgfdhgidgs
3?
x
ckhcjfj `kctgrjs cgiuhjs
x ?
F
Qkrk suikr g rjstkr ngs jxprjsdghjs rkcdghkfjs, pgr fg mjhjrkf jhcghtrkigs uh njhgidhkngr cgiüh y uskigs fks sdmudjhtjs prgpdjnknjs nj cgcdjhtjs< k n
c n
k
n
c
k
y
n
c n
k
c
n
Sd fgs njhgidhkngrjs nj fks jxprjsdghjs hg sgh dmukfjs, pgnjigs gotjhjr uh cgiüh njhgidhkngr kf iuftdpfdckr jf huijrkngr y njhgidhkngr nj cknk `rkccdóh pgr uhk jxprjsdóh kprgpdknk. Mjhjrkfijhtj jipfjkigs jf iéhdig cgiüh njhgid njhgidhkn hkngr gr (ic (icn) n) nj fgs ngs cgcdjhtjs. Qkrk ekffkr jf icn, `kctgrdzkigs cknk njhgidhkngr jh prdigs y fujmg `grikigs jf prgnuctg nj fgs `kctgrjs prdigs nd`jrjhtjs, uskhng jf iëxdig jxpghjhtj quj kpkrjzck cgh cknk `kctgr prdig. Jipjcjigs cgh uh jljipfg huiärdcg nj jstk tächdck.
JLJIQFG ?
Suik nj `rkccdghjs uskhng jf icn
Jxprjsj cgig hüijrg rkcdghkf sdipfd`dckng< = ?>
: ;5
>5
CKQÉ^ZFG ; CGHCJQ^GS @ZHNKIJH^KFJS NJ ËFMJO_K
SGFZCDÓH
Fks `kctgrdzkcdghjs jh prdigs nj fgs njhgidhkngrjs ?> y ;5 sgh ?> ? 3 y ;5 ? 3?. Qkrk ekffkr jf icn, `grikigs jf prgnuctg nj fgs `kctgrjs prdigs nd`jrjhtjs, uskhng jf iëxdig jxpghjhtj ksgcdkng cgh cknk `kctgr. Jstg hgs nk ?3 3?. Kegrk ckiodkigs cknk `rkccdóh k uhk `rkccdóh jqudvkfjhtj cgh njhgidhkngr ?3 3? y suikigs< 3
= : = ?> ;5 ?3 3
^D-53/> Qfus
= ?3 3
?; 3
?
?
3
: ? 3?
3 3
:
??
? 3? ??
?1 3
?
3?
>; ?3 3? >; F
=?
^D-50
Fks ckfcufkngrks mrk`dckngrks pujnjh nkrhgs jf iéhdig cgiüh iüftdpfg (ici) nj ngs hüijrgs, ksé cgig suiks jxkctks nj `rkccdghjs. Dfustrkrjigs jstks `uhcdghjs uskhng fgs hüijrgs njf jljipfg ?. IK^E
Qkrk ekffkr jf ici
5
?>
,
;5
)
?hn
JH^J_
Suikigs `rkccdghjs
=
;
IK^E
fci(@>)
?>
JH^J_
:
;5
IK^E
=
?>
@rkc(@;)
?>
IDSC(@:) ,
:
;5
)
;5
JH^J_
IG_J
JH^J_
Jf iätgng pkrk ekffkr jf icn pkrk jxprjsdghjs rkcdghkfjs js khëfgmg kf prgcjsg dfustrkng jh jf jljipfg ?. Fk ühdck nd`jrjhcdk js quj uskigs `kctgrdzkcdghjs nj pgfdhgidgs jh fumkr nj jhtjrgs.
:1
CKQÉ^ZFG ; CGHCJQ^GS @ZHNKIJH^KFJS NJ ËFMJO_K
@griufj uhk tkofk.
?hn
^OFSJ^ ;
Pdstk nj fk tkofk.
?hn
^KOFJ
;
JH^J_
;
^OFS^(@? ^OFS^( @?))
^KOFJ
;
JH^J_
^KOFJ(@; ^KOFJ( @;))
Fk tkofk kpgyk hujstrk sdipfd`dckcdóh.
JLJIQFG >
Sdipfd`dckcdóh nj suiks nj jxprjsdghjs rkcdghkfjs
J`jctüj fks gpjrkcdghjs y sdipfd`dquj< ? x : ?
x
SGFZCDÓH x
0 x 4
x ?
x
4
; x 3
Jipjzkigs pgr `kctgrdzkr njhgidhkngrjs<
? x : ?
0 x 4
x ?
x
4
; x 3
? x :
x x 3
?
x
x x 3 x x 3
; x 3
Cgig jf icn js x x 3? x x 3, iuftdpfdckigs jf huijrkngr y njhgidhkngr njf prdijr cgcdjhtj pgr x 3, fgs njf sjmuhng pgr x 3, y fgs njf tjrcjrg pgr x 3? y fujmg suikigs< x x 3 x x x 3 ? x : x x x 3? x x 3 x x 3? x x 3
x 3? x x x 3? x x 3
? x ? x ;: x x ? 3 x x x ? 0 x 4 x x 3? x x 3
> x ?
5 x 0
x x 3? x x 3
?? x ?
> x 3
x x 3? x x 3
F
Zhk `rkccdóh cgipfjlk js uh cgcdjhtj jh jf quj jf huijrkngr y/g jf njhgidhkngr js uhk jxprjsdóh `rkccdghkrdk. Cdjrtgs prgofjiks jh cëfcufg rjqudjrjh sdipfd`dckr `rkccdghjs cgipfjlks njf tdpg nkng jh jf sdmudjhtj jljipfg.
;.> Jxprjsdghjs `rkccdghkrdks
:;
Sdipfd`dckcdóh nj uhk `rkccdóh cgipfjlk
JLJIQFG :
Sdipfd`dquj fk `rkccdóh cgipfjlk< ? x 3
? k
3
x k
SGFZCDÓH
Ckiodkigs jf huijrkngr nj fk jxprjsdóh nknk jh uh sgfg cgcdjhtj y fujmg uskigs uhk prgpdjnkn pkrk sdipfd`dckr cgcdjhtjs< ?
?k
?
x 3 k x k
3
? x x 3
x 3k x
3
3
cgiodhj `rkccdghjs jh jf huijrkngr
x k
?k
? x
x x 3k
?k
;
3 x k
x x 3k 3 x x k x
sdipfd`dquj2 prgpdjnkn nj cgcdjhtjs `kctgrdcj ? k cgcdjhtjs
? x 2 prgpdjnkn nj
sd x k
?
o
sustdtuyk
x x 3k 3
k
x
x k
cgh
;
Zh iätgng kftjrhktdvg js iuftdpfdckr pgr x x 3k 3 jf huijrkngr y njhgidhkngr nj fk jxprjsdóh nknk, jf icn njf huijrkngr y njhgidhkngr y fujmg sdipfd`dckr jf rjsuftkng. Kfmuhgs cgcdjhtjs quj hg sgh jxprjsdghjs rkcdghkfjs cghtdjhjh njhgidhkngrjs nj fk `grik k ? o g ? k ? o2 cgig jh jf sdmudjhtj jljipfg, jstgs cgcdjhtjs sj pujnjh sdipfd`dckr kf iuftdpfdckr jf huijrkngr y njhgidhkngr pgr jf cghlumkng k ? o g ? k ? o, rjspjctdvkij rjspjctdvkijhtj. htj. Njsnj fujmg, sd kpkrjcj k ? o, iuftdpfdquj jhtghcjs pgr k ? o.
JLJIQFG 0
_kcdghkfdzkcdóh nj uh njhgidhkngr
_kcdghkfdcj jf njhgidhkngr< ;
? x ? y
SGFZCDÓH
;
? x ? y
;
? x ? y
? x ? y iuftdpfdquj huijrkngr y njhgidhkngr ? x ? y pgr jf cghlumkng nj ? x ? y
? x ? y
? x
?
? y
? x ? y x y
?
prgpdjnkn nj cgcdjhtjs y nd`jrjhcdk nj cuknrkngs fjy nj rkndckfjs
F
Jh cëfcufg, k vjcjs js hjcjskrdg rkcdghkfdzkr jf huijrkngr nj uh cgcdjhtj, cgig sj iujstrk jh jf jljipfg sdmudjhtj.
:?
CKQÉ^ZFG ; CGHCJQ^GS @ZHNKIJH^KFJS NJ ËFMJO_K
JLJIQFG = Sd e
_kcdghkfdzkcdóh nj uh huijrkngr
1, rkcdghkfdcj jf huijrkngr nj
? x e e
? x .
SGFZCDÓH ? x e
? x
? x e
e
? x ? x e
e
? x e
? x
? x
iuftdpfdquj huijrkngr y njhgidhkngr pgr jf cghlumkng nj ? x e ? x
? x e? ? x ? e ? x e ? x x x e
x
e ? x e e
? x
e ? x e ;
? x
? x e
prgpdjnkn nj cgcdjhtjs y nd`jrjhcdk nj cuknrkngs fjy nj rkndckfjs
sdipfd`dquj
ckhcjfj e
? x
1
Qujnj pkrjcjr cgig sd euodärkigs ejceg iuy pgcg, pgrquj eky rkndckfjs jh jf njhgidhkngr. Jh cëfcufg, hg gostkhtj, js nj dhtjräs njtjridhkr fg quj js vjrnknjrg sd e js iuy cjrckhk k cjrg. Hótjsj quj sd uskigs fk jxprjsdóh nknk gotjhjigs fg sdmudjhtj< Sd e 1, jhtghcjs
? x e e
? x
? x 1 1
? x
1
1
,
quj js uhk jxprjsdóh sdh sjhtdng, pjrg sd uskigs fk `grik rkcdghkfdzknk gotjhjigs fk sdmudjhtj dh`grikcdóh<
Sd e 1, jhtghcjs
? x e
? x
e
;
? x e
? x
;
? x
? x
;
. ? ? x F
Cdjrtgs prgofjiks jh cëfcufg rjqudjrjh sdipfd`dckr jxprjsdghjs njf tdpg quj sj nk jh jf jljipfg sdmudjhtj.
JLJIQFG 5
Sdipfd`dckcdóh nj uhk jxprjsdóh `rkccdghkrdk
Sdipfd`dquj, sd e
1< ; ?
x e x
e
; x ?
;.> Jxprjsdghjs `rkccdghkrdks
:3
SGFZCDÓH ;
x x e?
x ?
e
x x e? x x e? x ?
x ?
;
e x x x ? ?
cgiodhj cgcdjhtjs jh jf huijrkngr
? xe
e?
x x e x x x ? ? xe e? x e? x ?e x e? x e x x e? x ?e ? x e x x e? x ? ? ?
; e
jfjvkr kf cuknrkng x e2 prgpdjnkn nj cgcdjhtjs
?
jfdidhkr pkrähtjsds sdipfd`dckr2 `kctgrdzkr e ckhcjfkr e
1
F
Qrgofjiks njf tdpg quj sj nk jh jf sdmudjhtj jljipfg tkiodäh sj prjsjhtkh jh cëfcufg.
Sdipfd`dckcdóh nj uhk jxprjsdóh `rkccdghkrdk
JLJIQFG 4 Sdipfd`dquj <
3 x ?? x :;/? x 3 ? ? x : ? x :;/?? ;
SGFZCDÓH
?
;/?
Zhk `grik nj sdipfd`dckr fk jxprjsdóh js cgig sdmuj<
3 x ?? x :;/? x 3 ? ? x : ? x :;/?? ;
3 x ? x : ?
;/?
?
;/?
x 3
? x :;/? ? x : 3 x ?? x : x 3 ? x :;/? ? x : 3 0 x ;: x ? x 3 ; ;/? ? x : ? x : 3 ? : x ;: x ? x :3/? : x ? x x 3 ? x :3/?
nj`dhdcdóh nj jxpghjhtjs hjmktdvgs
cgiodhkr täridhgs jh jf huijrkngr prgpdjnkn nj cgcdjhtjs
sdipfd`dckr `kctgrdzkr jf huijrkngr
Zhk sdipfd`dckcdóh kftjrhktdvk js pkrk jfdidhkr fk pgtjhcdk hjmktdv hjmktdvk, k, jh fk jxprjsdóh nknk, cgig sdmuj<
; ?,
; 3 x ?? x :;/? x 3 ? ? x : ;/?? ? x :;/? iuftdpfdckr huijrkngr y ;/? ? x :;/?? ? x :;/? njhgidhkngr pgr ? x :
3 x ?? x :
3
x
? x :? x :;/?
prgpdjnkn nj cgcdjhtjs y fjy nj jxpghjhtjs
(cghtdhük)
:>
CKQÉ^ZFG ; CGHCJQ^GS @ZHNKIJH^KFJS NJ ËFMJO_K
Jf rjstg nj fk sdipfd`dckcdóh js sdidfkr. Zh tjrcjr iätgng nj sdipfd`dckcdóh js `kctgrdzkr prdijrg jf iëxdig `kctgr cgiüh. Jh jstj cksg, fgs `kctgrjs cgiuhjs sgh x y (? x :), y fgs jxpg; hjhtjs iéhdigs sgh ? y ? , rjspjctdvkij rjspjctdvkijhtj. htj. Jhtghcjs, jf iëxdig `kctgr cgiüh js x ?? x : ;/?, `kctgrdzkigs jf huijrkngr y sdipfd`dckigs cgig sdmuj<
x ?? x :
3? x :; x
x ?: x ;:
;/?
: x ? x x 3
? x :; ? x :3/? ? x :3/? Zhg nj fgs prgofjiks jh cëfcufg js njtjridhkr fgs vkfgrjs nj x quj ekcjh quj jf huijrkngr sjk dmukf k cjrg. Fk `grik sdipfd`dcknk hgs kyunk k rjspghnjr jstk prjmuhtk cgh rjfktdvk `kcdfdnkn< fgs vkfgrjs sgh 1 y 3. F
;.>
J l jr c d c dg s
Jljr. ;->< Jscrdok fk jxprjsdóh cgig uh hüijrg rkcdghkf sdipfd`dckng.
; 3
3
=
:1 :
31 3
>
?
03 ;;
>
:
=
?> ?1 :> Jljr.. :->5< Sdipfd`dquj fk jxprjsdóh. Jljr
: = 4 ;; ;? ;3 ;> ;: ;= ;4 ?;
? x ? ? x ? y ?
= x 3
= x >
?:
5
y 3
;?:
;?
r r ?
r 3
4 x ? 3 x ?
>
4
? x ?
= x 0
:k?
;?k
4 x >
: x ?
> x ?
k
5
k?
>
0 x ?
>
? 3s ? x
3t t ?
;
;0
> x >
5 x =
>
0 x 3
0 x 3
?:k?
?
x
4
:t t ?
4
y 3
?=
;1
3r r ?
?4
?r 3
3;
> x ?
5 x
3?
4 x ?
?1k
>
33
?k
;5
;
?
x ?
?1
3
x
>1 t ?
>
> x 3 x > ;? x
x ?
4
x ?
>
:s : x
?
3:
: x
?
? x ; ?
x
4
:s
?
x : x 3
3=
?
3 x
>
p
3
p
3
x
x x
k
y ?
;
y;
? x
x
:
x 3 x
?>
4 p
;5
?
;
?
31 0 x
x
>
: x ?
x
4
?kn 3oc
>
?
u
x 3
> x x r s
x ?
s
x ?
=
x ?
35
r
s? r ?
x
y?
x
w
: w
3
r
y?
3
>1
?
s?
xy xy ; : ? x x ; x 3 34 = x x ; x 3
3u u
?
?
0 ?w
;
5 ?w
? x
0kn 3on
x ?
30
3 x
0kc
3
3>
oc
o
;
? x
;
x
?
?kc
k
;
0
? x 3
?5
?u 3u
: x
?0
; o y
x
0 x 4
5 p
? x 0 ?
> x >
> x
4
?
? x ; ?
t
3
? p
u
?
3
?
3 p
:
? x ? 5
;5
5
x ?
y ?
s
t 3
? x ; ? x
; k x ;:
>t
t 3
o
;0
>
3 x ;
?=
5
3 x
3s
;= x ;1
?= x >
k
x ?
4 x :
r >
?:
?
k
k3
?= x >
>
k3
y ?
;1
3r ?
3 x ?
t
?>
=?
? x ?
0
?3
>?
??
;
:
on
::
;.> Jxprjsdghjs `rkccdghkrdks 3
>; >3 >>
x ;
k
x ?
k
?
k
x k
x x ?
3 x
x x 3
: x
x x e3 : x x e
:; :3 :>
0;
03
e
x x e
3
;
;
3
x
>0
e
3 x 3e
;
> x ?
x
:
0?
?/3
x
x ?
> x 0
? x
x e
x
e
? x ?e
3
? ? x 3 0> 3
??
x :
x
Jljr. 0:-05< Jxprjsj cgig uh cgcdjhtj.
0: x 3 x ?
00 x > x
0= x ;/? x 3/?
05 x ?/3 x =/3
> 3 x ;
e
x x ?
;
Jljr.. 04-5?< Sdipfd`dquj fk jxprjsdóh. Jljr
: ? x 3
04 ? x ? 3 x ;>3 x ?33 3 x ?>> x 3
e
=1 0 x :3? x x ? >? x x x ? >?30 x :?0
Jljr.. >4-:>< _kcdghkfdcj jf njhgidhkngr Jljr njhgidhkngr..
>4
Jljr. 0;-0>< Jxprjsj cgig suik nj täridhgs nj fk `grik kx r, nghnj r js uh hüijrg rkcdghkf.
e
:
>5
x
>?
x x e? 3 x x e
>
>=
;
x k
;
>:
3
? t t :
:1
? t t : 5; x ?
;0 y ?
:?
3 ? x ? ? y ; 3 ? k
? t t > ? t t > ;0 x ?
?
y
?
? ? x ? y
(Sumjrjhcdk< Iuftdpfdquj huijrkngr y 3 3 3 njhgidhkngr pgr ? k? ? ko ? o?.)
? o 3
=;
x x
;/?
> 3? x
?
; ?
;
3 ;
?
?
x x
;/?
>
=? 3 x ?;/3?> x :> > x :? ;3 3 x ? =3 3 x ;0 ;? ? x :
?
;/?
;
? x
>/3
? x :;/?03 x ;:3
x x 0
> x x ?
;/3
43? x
Jljr.. ::-01< _kcdghkfdcj jf huijrkngr Jljr huijrkngr.. ? k ?
k
? o
:0
?
o
? ? x x e
:= :5 :4 01
3
?/3
3 3 ? x ? y
; x ? 4> 3 x x 0 => x
::
? x
;
? ? x
? o ?
o
? c
?
c
x x
==
e ? x ? x e e
? ; x
e 3 ? x e
e
? x
4 x 3 ? x 30 x ;?0 0 x ;0
?
x ? ;>? x x ?> x x ? ;3? x =0 x ? 5
? x ? x e
x
0 x ;3?= x ?
;
e
? ;
=:
3
(Sumjrjhcdk< Cgipkrj cgh jljrcdcdg :3.)
=5 =4
x x ?
?3? x
?
:>3 x ?
?
??? x
?3?
x > x x
x x ? x x ?
;
x 3 x x
x x ? x x ?
3
?
:3? x
:>?
; x ? >;/33 3 x 3 x x x ? >;/3?
>?/3? x
View more...
Comments
