This document contains algebraic equations and expressions involving variables like x, y, z. It explores relationships between variables, simplifying expressions and solving for unknowns. Various steps are shown involving addition, subtraction, multiplication and division of terms containing variables and parameters. Solutions or equal expressions are presented at each step.

1. (1• ucir.°)S°3
(x quas)i_visoa -zy
(xic uastsoo)zuas = A .05
xji _quel x = •st,
- _x = (1x)uas -s¿
• •
I —
= 'EZ
(X SOD - X UDS 3),..,a = a -61
xr uasis- =
( rx ± )Das
(rata)ui = ri
,*9Z
) = *c:
'ZZ
=.8 I
OZ: ur1 +
oz, Das
(1 "9//' 'YzUDS t = 'LS
DI
c
e /va4
•ouasoo uppunj el eied uompe el neinuncij el dlualqo •(z) f anuanoua '1 + ny,= ( ni !S 15
v uas X SOD SOD x uas = (y + x)uas
~Te el op Eintung el xenuap iy (q)
-ouas uopunj el Bird DIL~OdSDI-103 EITIULTOJ U1 Eilualqo
alqop opbSue iap ouasoa lap emulo; ei Juis.pap Ey (e) -89
- x q - x v - x
(A-c-
+ rZ
ul —
=n
.9j7
1717
"Zt
'01
-1E
.9£
- Ex
x
I Mi./
anb a.psanwap - x)(q - x)(v - x) (x)f ts '19
•l aluaTuad auap aluaBuel ElDal
El apuop i = zÁz., zx asdpa el anos solund sol auuartaua -99
umuozpoti rloai run sa aula2uel
rl u!,-(-; () -x soo uas = muno ei ap sonind anb ua? •s9
•„. f Á ,l'f ap srage.r2 srt opuri
-rdwoa aiquuozri sa (e) oscaur lr eisandsai nsIs anbppaA (q)
l'U/ uas
„Y + ,x
C-
+ X")
- í= ,ax
uasDn)urpie =
=
11.
a.nuanoua -¿Av, > x > - UE1 - 17 = (x)f !s (e)
,f Á sensufs se! opurJ (.,.a)soo = *ZE
XitIDS - Xr,S00 = XZ SOD
-alma aiquuozei sa (u) ()spur lr elsandsai ns 7 anbppaA (p)
mued rausp.0 rl ua sal
-raSuel srloal sri Á muna el opurfnqw (q) os!aul la ansrui (D)
-(-17 -17) Á (z. ) solund sol ua x - gi•x
ruma ni u salualum SEPOI SE' Op sauopunpa aquanDug (q)
"(x),./ ziT11 - c/`1- = !S (r) *E9•
"soputuawo3 uleni
•-cluild ukts!ut ut LID ,J. f Pl-hcbG •(r) , apl.!„„,••?A- = (A-) !s
( '0) + Z) = '19
(1 'Z-) '£1 = + + '09
•roupazisa as anb olund ¡a
LID rAlna ri r leullou F, alualuri wuji salolarn3D JultuFf 19-89
so imu3r3
NOID'v'AD33C1 3G SV1D3'd £ 01r11.NEVI) Z97.
(x£ qsoa)ui = A -st
(zx)quas x =
L(£ + = S .117
- +
(O uas)zuel -6E
(Ex + I uel)uas = -LE
(g z.voloa 'SE
xc uri xg Das I ut = .c -EE
(rt)i _uel x = [E
(1 - x£)€(1 + xZ)
.0£ Auras - x uas Ul A .15-t-
+ Ex)
sco) = a -SZ (xZ. + 1)1101 = n *L1
= .17z, uas + 1 SOD
erg aso)uí = -91 .v = A..7 + „J'a-
( 1 - 1 4- .25
-
ua L'AinD v:i E PIUDIUU
( LO) t + I // '65
•oprp mund
ap sauopenoa a.nuanaug 6c-1C
(x- nos - .guas
1
'( 'ti
z(xz, uasair) = *¿
xu SOD = -01
= 't
SOO l• A = • I/ j
—
A- -6
oz,11:;,'d = •L
+
A./‘ G)
- X = A.
01[1310 09-1
(Z: + IZ - =
1•¿P
"t7
(a- tun)soa = r: -z
(ir,)um
• • al;! PpleAg • •cpg
Tra(u x) (x),„, f. SDDUalltD 've)A. = (1.).[ anb
gowap und (LL rtqlcd) rny,,ttiolutu u9pDnpu! rl anblicly
"(x - Z..)/1 = !s --111!m-la 179
I = ,yr 2J-•w-7.1113i:3 'ES
.(9/1),15 UOS R = Y3 !S 75

2. oiaPIP-'DA "11
osied -s cuapepiaA •E oiarrepiaA •1
OSIEJ-0.19prp.10A 9p segun; a.id
SI -
> 1 > O :Z < I (a) ot (P) £Z (o)
> o tz < 1 (q) = (i)v — ziE = (1)a (E) '68
[(Si + Jm)uas 019Z + (3 + .e»)so3 — r a)],,_ay = (1)v
'[(g "t'as (g ")soa d],„_ay— (1)4
x- + zx — = •sg
(0 'e —) 'es (t7)(rt, so3)(x17 uas),8((x1 'te
,[(1-)6 + (1-)f]
'6L (x)6Ax16
,:[(r)ax),6 + r[(x)61(x),./.
,?( ,d),B 'S L (1 ),b(-1)5Z •£1 (x),fizx + (1 )617,
olápepnA '6 osied "L
19Z VNIDVd w E 0101IdV3 130 OSVd3d
(ZP + I)uI) 'SS
n qsont, — n quas z = rC (q) •es
ovE.oc. (q) ZLS£'0 (u) '1S
I + t'/`x vp
I —
(£/x)i_quas — I)fZ —
c(x.LISOD + I _
= r),9aguas ( XrLIDDS
1717 (q) Z (e) '69 W— 'fi/1'0 '(/ 17/11) '59 (,a)quei (,a)zq3as ,az— = (1),f 'LE n quas nil.ai = -si
01-
01
01 (p)
8 ± =-. ± = (q) •
x£ — 01
x —• Z
(u) 'E9
Z+x = =
+ 17, = '65 £//"1" — 1 + =
uelpz;
iC/rxg— '£5 1— 15 '6P
(n)zuas u„,.,9(£u„, ,,1)11Ds £-
1 — rtitias /‘•
LP x£ 1-11-121(x LIMO)
R(£ ± X) I + XP
(z,s — rgs — — x) 11
(o uas)roas (o uas)uel 9 SO3 Z '6E
+ itz.
rx£
uul)soo .ze
. (S + Ex£),:3s3 x9— *S£ xSps S TE
(x17), _uei • ti x SOD x uas — X100 -61
z x9 I + I
ul (rZ + T)) I + (dx)soo x•LZ
(A7x)soz) A" — 1-17
z.-(T — X) — .£Z Ul '1)(£ U1).,„uvE
UOS ,.,a(rD
z0Z, +
I) -61 'LE•(1 — 0 -c; uel) oz 32S Z
—
'51KYZ — r.i — I (XZ Ovia
Z z( zi I)
•1 I '6. st'as — SOD
I + AY`
OZ S03Z: •1
(1 + Z)Z
LZP£ 1-PZ
(£ — zrZ)7(S + zx£ — x)x9 "I
17"
soppAah
x qum = (x), -tt x 1103 r = (x),f •ii
O (I) .7) (q) QQ (2)
1 (3) O M (p) <XI (3) I— (q) T (u) 'E/
x qsoo 'S = x x qoso = x quas = x goas
0 (q) 1 (E) *s
989z9-£ ~ ( z_a — (q) c(e) t I (q) (:) (u) •i
652 VNI9yd 53 I VE SODI311313
(dm °poi, (q) '8'17 (E) 'Et
(q) qi-EtZ (u) 'LE
810'0 1£U-ID 6LI z.111-179L I (q)
ZIO'0 t,11-13 LZ ^ 2/1178 (u) 'SE
%YO '900'0 `r1u3 9£ (q) %I '10'0 OLZ (u) •E£
S96.0 06/1/ — I V/ Z0'17 'Si 807;£ ti
szro— = = ti
8'0 = A:77 `17.9.0 ,CV '61
(q) rP zoos = ^P (u) • Ll
1010'0!TO*0 (q) = <CP (1) "S I
£(1:-1 + I) z(T n) -_tp = (q) np (u) ti
Z-
01
,x)quas (ér)gsoo ryz
3CI SOIDIMJ313 SVIS311dS31 I 3DICIN3dV tUl 9LV

3. E- = zE -F. - - E.IZ 'ZS = S 5UDS ± SI SO3 •-tc
-sp auFulaap `z1 X I c solopaafa soI ua
zi£_(dZ + zdS) = b "OS z = zbE - bdt
•bpldp aucrmapp `0$ Á 6{7 solopiala sol uH
x -
x + I
zA.
cn~ —
1.12S -I- 1 = a .9E
E( I - nt)si
= .0£
'95 (J) zuas z_x =
xs 103 ry = er .9z
,(1 x)oso =
uosx.A.z = .zz
z( _r_Az
1 + YZ)
= .Z£
I + zx-Z (x)2 179
I +
= (1)f '£9
-uotonnjap eI opuesn epeApap El aup.uialap `179 X Eg SOI3T3IDID SO1 ua
epenuap ap uopluplap el ap u9penldV
-(8 '8) olund Ta tia zap/e(,/, atnuualop '17 = ,/,(C E/Fi- ts 'Z9
-(i 'o) olund ¡a ua ,x--ppíj ap aojen la au-nuialap `x soo z =(1. ,((!s
= e + izO
tir(L + LO) = !s `0 = i no ip/jp ap .101" ta OTILL1010a
'(0/1.1. S')UDS g =
(Z -) nos = nt IS O = S' ua splinp ap .101EA la DUIUSIDIDG
«ui(nz + zn) =
is = s!s z = n ua np/sp ap aojen la auirunalaa
+ 51 = X XZ UDS E = ft. ts p = 1 tia ,ippCp ap Joren la ou!uualau
I = r(cx '9P I =d21/- '5P
'69 SI = odOI + sit,xS .1717 aL = - (C17 + c'Y TI7
Z = rc z1( + (Cr ± *Zt T = (C£+XZ+ (Cx'Ib
'85 -eEolidun ucgenuap aluetpaui xp atquualap `817 E 117 SOI0I01DrD SO1 ua
LS elpyidwl u9penpaa
'09
x soo
O = x .a
(x)f
I = x .3
= x 'Vil xy, -u
ap opep101EA ¡O
no saumoeuRwoo sawa!n2Is su' ap sepenriap selatuud se! auuulalau
S/ I £-
Z- 6 0
(x),.f (x)f
=XXO=XU0 SOJOJEA sal
-ua!n2ts sol uouan epenuap elawpd ns X (x)f umunj uf anb e2uodng
= x '((x)8 x)f
= x ziz((x)/ = x `((x)f ).5 -a
O = x 1((x)8)f 'P I = x (x)8.3
(x)f
= x `(x)z8(x)f = x `(x)g - (x)f9 -E
ap opep10IEA ID
ua sauotorUiiutoo saluatn2!s su' ap supenpap seiatupd sei au!tuialau
i7- z/T S E 1
z/I E — 1 1 0
(x),z (x),J. (x).? (x)f x
1= x ri 0= x ua saioren saniain2!s sol
nanap sepenyap selaux!id sns jI (x)8 `(x)f sauo!ounj se( anb e2uodng 'SS
sepenpap ap sonp.awnu saJoieA
- = za-ppQp anb ansonwap `oÑanq -y
= zic -q 1 = £A. + 11"- -E
:Rylandurr uopenpap 91u-omaní ,xppc_p DIUULIDJDa 'ES
E/I-(xE éc>0 + E) = (C. '01
0-(7 - xE)i,h(t. - rE)OZ = .8E
(i + 61/ + 0) UDS = 'OZ
O SOO OZ = .1 '81
(ziE + I - j) s3S3 = S "91
(.9 loa "pj
Z
X UDSX LIDS Z
x znas - xzuel z = jI -ITZ
.ZI
— ?A. iI
01 + - 5-6=
!/.
5(50 0 0S3 •8
Z
£(1 + 33S + ¿O) =
i_(X t)(c — = (c. .9 (XZ + zx)z( + = jI -S
(Z11 + ZX)1 1x = .1
tx £.0 + O - £ = d 'Z xSZ*0 + zxSZI.0 = ((-
'017 E I SOIOIOIDID SO1 ua SDTIOIDUT sud ap supenuap se! atuuualacr
sauopunj ap sepenpea
1 = x `(x),1 01 •
O = x '(x un S - I )f 'P
x `(x)f "ni
z/z(xz nos zz-s)
= '6£
I + xZA (I + xz) = 'LE
1 9 coi
0 UDS J — .9/
ZX
X + 5XP - .££
( 1:"^
1
z
+ )
- 'LE
( I +
- s '6Z117
(5XZ) ¡UDS 5X =j 'Lz
rxlon S = j 'SZ
z(x-Was = ((' -Ez
_x oso rx-z •Tz
uas = -6T
0 UDS 0Z/. = -Li
c(/ uEl + i oas) = s -si
(1z - vS00 = s • EI
•(f/x = IPPCP I +
anb ansarunap 'T = - zxap elmiduu uolo-enuap aluEipapy .179
XLJ... LX = •17
sepenuag :E o-in4Idej
9L

4. by + zdE bp
61dd1'– 179 = dp
£/te(17 xt1' + x
EP 'IP
Z + Kt7 — rxE— Z +
z(1 — o soo)
z( + x) ((z
L1'
x 'S1'
[zis(xz uas + zxg)]
6 6£xz soo xc
I + xZ/.£ LE
Bs/Pti 9/1– = 1/9/zOP `°°s/1)21 9/1 = TPOP (3)
20s/PEJ 59/8– = /PizeP `a3s/Pni S9/8 = IP/IOP (q)
Bas/IJ SL8.8— £1/_/Z1— (E) •£17
á‘11!u1/11!
'IP
2
sosipel I— (3) 23s/z$ 1•65_ (q) 205/11z7/13 0(EZS) :e Zz
aluapainap `2asituo £I/PI— (a)
anmsuoo `2as/uuo O (q) oluapán ‘Oasizinni7T (E)
y2 v _
ciP I
+ 41 0 uas q +
!13– o uas q
vp
—IP o soo qv Z = --1P (a)
OP I VP
y2
oo soo qv 12= izp_1 (q)
1
1;5/ osoo qv = (E)
zi( zr/- IP
xP x (q)
7/2 Zif
xP X = ST9 (E)
-6I
IP X 119 (3)
eip t xP
LI
•IZ
tu z‘f — /f9z/•. = (q)
Tul mo Z6171 = (q)
zupni7 1891 /9917 ua olimpo.°
2as/U II TE Tul/z13 u01' `e!w/13 1
unuim 1L'88Z = 1/9
S 'IP
ititZ
Illuita13 611 I =
2as/k1 00S — '6£ 23e/u1 S— •LE
'S£
*1£
(3)
(E) '6Z
(e) •LZ
Z—
+ 1Z)
T9 T 19 £/ '69 O •L9
17/£ (2)
Z/6 (3) Z1 (a) 17/1 (P) ZI /S (3) Z– (q) L (E) 'SS
I – i(zP 1711 – 1(zP
x zrp (q) = z179
"1)(1 — -/Z) =
gp
T9 „
"1
o uas z— •9£
Z11(
X -1-,)zn
I EG + x) El8
TE .1£ 6Z
1— x– r (I + i)—
(zx)tilos rz + (zrz) soo (xz) um cx8 -Lz ( x)r3S3 X0 I – .SZ
[Z--x Z(XZ) 91 lz(n) 035 z/IX-.1 .EZ
(-1)109 ez--) Oso + (–x OSO X
Z) °
1Z
9.Z/. 19 112S OZA
6I o uas + o SO0 e
,(1 Wel + i ogs) oas)c
(/z — 1) uas (iz — 1) Jon 8
+ I)1_/_ Z.
'6
•xy + i = (x)7 sa O = x ua uopuzpuaup El anb rogru2ls olsa
= (0),J anb ol aod _1(x + )3/ = (x),1 ‘sVaind I = (0).i
zI
y xT -u s— .6 rZ 'L
– x = (x)7 .s = (x)7 T £1 — xim = (r)7 'I
SLI–ELI *dd '6*£ u9P3aS
OZ/".SOO
'LI
'SI
xuEl x zOasZ •II
(O Wel O OOS OZ) z( + 9 005 + ze)E
+ X-17 ZXZ)(I X)Z .9
(Z X)X£ S •° XSZ.0 17XS "I
O81-9LI •dd 'enpead ap soppia[3
-rima ti ua pnnu2rin utuspn El ap oIcitueo un ap ()paja la
SDODA 6E ap lopapanu auap runi el ua pepanui2 vi u vino]) ucip
-uniaou El ua omtuuo un anb olloci Luí E italt sa UOZEI
%£ '617 %– •L17 %17 (q) °AZ, (E)
Eu1 9•S9S AP *£17 %Z (q)
zui 1180.0 (E)
1-P°-'- Z = AP '6£ x72 °xZI = SP
z°-¿-2117 = AP 'SE SI/1 (3) S/Z— (q) E/1— (E)
1E0 (3) Z (q) (E)
I y (3) - (q) 1 ti (u)
x
xp ((x"z – i)voo (z-A2 – 1) oso)
xp(1)70as (J•17)
ix -
xAz x KA.E
xp (x, S) so3 =1 Ez
17, z(zx + I)
•6I
xp
zxE) 'GT
zrZ — Z
£00.1 (q) 10.1 (E)
•nuatune X `las/sumo z/E (p)
1/9 I _ 1P I = 1P (3)
IP A AP ) 1 2113
,Sas/clum (q) 2asivion 1 (E)
y2 _az = 1p (3)
11P AP
—11-111-z
Jp
(q) — ruL = — (E) • £1
aP AP 11P AP
u /cut S£1– (q) Tui/zul()81— (E) -II ETRE '6
Z/E— 'L 9— '9 01 'E 5- = —1;-1p
£91.-091. *dd `8°E u91-330S
xplKp efp ifrZ £A. ,z1(1 £ zx xP
1 = xP ¿LIT + xP 1(X.Z + £1( e(P
(1- st
L
s
Z
– = tu (z— 'E)
_ w !—
a
= (z– `E– ) !
Z
– = (Z £–)
LZ LZ
'15
L£
'ES
'1£
'6Z
•LZ
'9Z
' IZ
'5I
£1_11,. ludan wawnu uoo soppiaca sol e sqsandsa8 :s op-p.IdeD