1 Numeros Reales 1. Simplificar al mсximo las siguientes

 01(69'7!&""#%DA$'&)9(*"0&)3L+-(B9',/&).9>"13M9>012&4!35"9E36&)7D!8!&A"O9'NQ:<PR;=:A9>D!3?$'9@&).A:!AD!(B9'0136&)0D!:A9>9'-3'CA,)3:!D!%"&4$E(=&)&T:AD!SU8A0F9%V4&4&)3B0G0)&H(B9'%3&)D!3B90F&G9'I&WJ.AXY"0&)13&A9C<.D!!9>(B#!9>:!3B"0$>:!K9': 3
D%&)D%&43360:Z:U[A19>(B03(B9'&)9>3'
\ &<]_^a`cbed@f'gih5jk^l`mdnbef>gohpbq^l`mfnbedgohQjk^a`cbednbrf'g>^a`cbed?jsf>gtbe`<h/^ldnbef>g'^ld5juf>g
\ Xv]xw@wBzUy { b {}{|zUy w
\ $~] ww yyRwzU {{ yy{ j€j€wwwyyzUzU{ {{ yy
wzU{ `‚bew  d {
\ Dv] `‚brdnb ƒ
wzU{}z€…i†J„ ‡
ˆ‰c9'03o;=(=&4(Sm8!94Š
‹+ŒŽ=- P ‘ Œ%’ j m’H“ ^ Œ j  g'^ Œ%’4z%ƒ b Œ%’/z h  b Œ%’4zU” h bk•~•~•Jb Œ h U’/zU” b Œvm’4z h b m’4z%ƒ g
–A—~˜*3+03B"X!9‚9>:!$'0):m;B(=&)((69E&)"9'3&™WšXZ;=&)9>3LSm8!9)Š™w  ƒ { “ wƒ b›{Eƒ œ
 ‰c9'F8!9'3o;=(B9HSm8!9)Š
\ &<] ŒŸž ™¡ Œ¢ž¤£ Ah ¥ ž¦
\ Xv] ŒŸ§©¨=-§¦¨F¡ £ Ah ¥ ªq« Œv
¬­n(B0X%&4(Sm8!94Š
\ &<] ¨Gž¦ŒŸž€®¯©T¡°Œv b ®H¯©Œ b 
\ Xv]`<h±brd@h “¤®5²Œ h
b  h “³®c¡ ` Œ brd ´¯µ®
\ $~]` § ¨ d §©¨H¡ w6{ ¶¶ jµw{ yy jµw{ b ® ª ¨
\ Dv]`‚brd “¤®M¡ `·±bed=· ª ®~¸)¹Aº \ :!DIŠ^a`cbedgi· “¤® ]
»A‰c9'F8!9'3o;=(B9HSm8!9)Š5`<h±brdh±brfh “³®5²ZŒ h
b  hpbe¼)h ž©½H¡ ` Œ b¦d  bef¼ § j‚¾
¿ ‰c9'F8!9'3o;=(B9HSm8!9)Š
`d Œ Œ bebef d   bebr`mf>¼¼ ““ ¨¨ Á ÂÂÃ
f Œ beŒ b`   bebed@¼¼ ““ À ¨¨  ¡ ` ” brd ” brf ” “Ž `md@f
Ä
ÆA‰c9'F8!9'3o;=(B9HSm8!9)Š ‹ `  d  f  P ‘  3B9$'8A1!"9)Š
\ &<]_^a`cbednbrf'g>^Jwƒ bǃ{ b›Èƒ g ªkÉ
\ Xv]Ê^Jwƒ j ® g'^~{ƒ j ® g>^~ȃ j ® g ª ¹šº A&)X!"9':!D!0TSm8!9H`Ëbrd±bef “³®
\ $~]`mdf “³®c¡ `‚brdnbef ª ½
ÌA‰c9'F8!9'3o;=(B9HSm8!9)Š
\ &<] Œ h±b  hpbr¼)h ª Œv b  ¼Mbr¼ Œ ‹+ŒŽBÍ ¼  P ‘ 
\ Xv]Ê^a`cbedg'^ldnbef>g'^lfnbe`Ug ª ¹ `md@f ‹ `  d  f  P ‘ 
EÎA8!8!:+$'08!:!9>7<(B&4+3B09ËÑ-Sm8!CA9ËWš8!Sm:8!9$'8Aћ9'(B3B+90G™Ï€8A9>369ËV9™&G8!369>8V)9V)$'9'0Ò:š$'0)8!:Z:!&F8A:%V&™9'"0V$>9'"0D%$>&4DšD%&4Ð Dšƒ \Ð W´9'\ :š9>:"2&:!™9'&F(B3B9>1$>;=&&<]5"$':!0)9':Z&F(6(B9'9>36$>Í;=&<9>]?$>;=$'00:&
(B(B9>9>3B3B++9'9'$>$>;B;B0Z0´&&-Ó×8!:Ÿ$'$>0)8!:Y9'(68!Í:!0&TÓTV)9'O0NLU˜n$'":mD%;B&)0D:!$>Ð 9'3ËbuD!9GÐ &4C%$'9>8!39>DA(BD!9'0´$'"('$>C%036:Ôt2&2&4-1&)9>$E,)0:A3Qh $EК&1&GD!9™2&™ÕV9>9>ÖL0U;=$'0)":ÔD%&)ÏÇD$'3B9™0:ZF2&8!™9>$>V)8%9™&)$'tÏ0:
3B9H™8!9V9$'0:Z(B9>3B+9'$;=0´&TÓ¤;B9':!9>1ƒ0)3Sm8!h 9HÐ “ Ð ƒ brÐ h \ 9W´D!93B8A-&GD!9ËV9>0U$'"D%&)DD!9HÕM9ÖL;=0:v]@
˜8n!:šÒ (B\ 9'&&4$';=8!ØVU&)Ù3D%6&)9‚DTD!9>9'3B:A+0)9';$'&F&)+0\ ˜n(?f':!]@3oCA;=3B9>":´:v]n9'F3B9‚X%+&)0(B7)3o;=0!8!C&36HÙSm369c8!9‚;=0:A10™&9.Ð 3o;=“ 9>:-Ð V9>“ 0U$'h D!&)D!9'35-&EW)0(B9>3?Sm8!9‚&D!9M2&
f
W
B
3
Ë
9
)
&
A
'
$
&
&
9
W
!
D
‚
9
B
3
A
8
&
h
ƒ
”
“
m
Û
)
¸
½
§
D!8!919>7V)0T9'"0à|8!$>9D%:A&)9'DA$'9'9>33=&)D!(69101ÕMÍ9>0ÖL3o;B;=08!:Ú&)(3698!:%;B&9':A:U918A9>SmV48!&-919ÐWšD!93B8!f1&DAfš9HÜÞÝ!V)9'&)0X!U(B$'"&)D%:_&)D!V9>9'3'"0$>˜nD%&&4GD!9'9'33Ð 1“ &~W)0á (B9> 3Fá Sm8!\l91ä f/9WßØC
y
„
±

â
â
ƒ
„
ã
y
D!93B8!1&TD!9ËV9'"0$>D%&4D!9'3LD!9H˜n:A36;=9>:v]@
‰c9'F8!9'3o;=(B9GSm8!9G9>:Ÿ9'3o;=9G$'&)3B0´Ð:!0šA8!9'D!9F3B9'(c-&EW0)(cSm8!9G$)CÍ9'3‚DA9'$'"('CÍ0-Sm8!9G369™!"D!9FD!9>10)36;=(B&)(
9'3Sm8!9)Š
¨T¯ Ð ƒ ¯ f ²¢¨G¯ Ð h ¯ f ¡ ® Ð ƒb brá „Ð á h y ¯ f
Èy
)‰c9>;B9'(61":%&)(L0)3L3B7)8!9>:m;B9'33B8AXÍ$>0:/å68!:<;=0)3MD!9P ‘HŠ
\ &<]¢æ ŒŸ P ‘ ¸JŒ h±b Œ j ” ¸4ÛT§¦¨ç
\ 2]Ÿæ Œ¢ P ‘ ¸/Œ hQj Œ b ½¯ì¨Uç
\ Xv]Ÿæ ŒŸ P ‘ ¸JŒ h b Œ ª j ®J¸4ÛAç
\ -]Ÿæ Œ¢ P ‘ ¸/Œ h b ® ª ¨ç
\ $~]Ÿæ ŒŸ P ‘ ¸JŒ h beè ŒŸž€®'ÛAç
\ :v]Ôæ Œ¢ P ‘ ¸/Œ h b¦è ¯ì¨ç
\ Dv]Ÿæ ŒŸ P ‘ ¸JŒ h±b ® ¾ Œ b ½éGž©¨ç
\ 0<]Ÿæ Œ¢ P ‘ ¸ è Œ hQj Û<¨4Œ b¦ñ)è ª ¨Uç
\ 9~]Ÿæ ŒŸ P ‘ ¸JŒ h ª Û)Œ b ® ¾ ç
\ v]Ôæ Œ¢ P ‘ ¸ jr¾ Œ hQj ®~¨4Œ b ¾ ¹Gž ¨Uç
\ à=]¢æ ŒŸ P ‘ ¸JŒ h bë·ê § j ½4Œtç
\ S]Ôæ Œ¢ P ‘ ¸®~é/Œ h be¾ Û)Œ ª ñ ç
\ 7m]¢æ ŒŸ P ‘ ¸JŒ h5jrè ¯ì¨ç
\ (=]Ÿæ Œ¢ P ‘ ¸ ¾‚j ½4Œ jr¾ Œ h ª ¨ç
\ Ýv]Ÿæ ŒŸ P ‘ ¸JŒ h±b Û É ¯µ®EÛ)Œtç
\ 3=]Ôæ Œ¢ P ‘ ¸®~¹/Œ h ª ¾ ®>Œ juè ç
\ í]¢æ ŒŸ P ‘ ¸JŒ h §q®E¨ç
\ ;]Ÿæ Œ¢ P ‘ ¸ ¾ é/Œ jrè Œ h § è ç
\ å=]Ÿæ ŒŸ P ‘ ¸ h”R£î !!ïï ª ¨ç
\ 8v]Ôæ Œ¢ P ‘ ¸)½4Œ h
b ® ¾ Œ ª jc¾ñ ç
\lð ]Ÿæ ŒŸ P ‘ ¸JŒ h beè Œ beñ §¦¨ç
\ VA]Ôæ Œ¢ P ‘ ¸ è Œ h b¦¾)è Œ beè ¨Gž©¨ç
ˆ
~ˆ‘&):<9>;=3B90ØV8!:!9>(‚"02&:!)9>333BDA"79H8!"":<9';=:<9';=(o9>V43c&)0:A3>9'$'8!&)$'"0:!9'3>CÍ9@.!(B9>3=&):!DA0š9'
$>0:/å68!:<;B0´3B0"8!$'"K:Z$'0(6(B9'36Í0):!D!9>:<;=9™9'D!òN
\ &<] ï £Eh zUó ¯ì¨
\ Ýv] £ £y zU ”õh £ ž ¨
\ Xv]Zè Œ j ½ ª ¾ Œ b ®
\ 2] ƒlï öBzz÷}÷}£ £ ž óõ£Eóõz£ ·
\ å=]Ê^ Œ j ½ g'^ Œ b¦¾)g'^}è‚j Œ g ª ¨
\ $~]Ê^ Œ jr¾g'^ Œ b ½ g ¯ì¨
\lð ] ø £EzUø óB”izmù ø ££Eùz h ù ª ¨
\ Dv] Œ h±b é4Œ j ½ ª ¨
\ 9~] ½4Œ hQj Œ beè ž ¨
\ 2]Z¾ Œ ^ Œ ó jrèg
j ½4Œ ª è Œ h5jr¾ Œ ” j ®'Û)Œ
\ -] £ y zU£ú ”õ£ £ ƒlö §©¨
\ à=] h £ ô  ƒ ž ”õ£E” z ·
\ 7m] £· bµ£Ez%ó ƒ ž £” b ®
\ :v] £ y zU£”õ£  h j £ y £ ”õ£ h  h ¯ì¨
E–A9'ûM:Z:$E$'&)"D!9'(o&;=0G":!$'360);=&)1:<9;=;9Ë&™ü?%DA&)9'3BI;&)=(=",G9'$>9'Í(B$'0G&G369'D!(B9Ë,A2&Š F;B9'(6(=&FDA9H0UD!0™Sm8!9Ë3B8ZD!"36;&4:!$'&FD!9Ë9'3o;& \ 9>: ð "K9>;B(B03=]
®~¨AýÞ¨¨¨ýþ¨¨)¨ ü h b ½¨ýþ¨¨)¨Aýþ¨)¨¨ üÙb¦¾ ÛAýþ¨¨)¨Aýþ¨)¨¨
19L9>3=:!&40XÍ(L90Sm8!79?8!9'&)A$ÙS>m08!9T9>;Þ&‚ÎÎ$ÎAÝAÞ0Î$'Î&)Î(=±,cD!$>9 0:Gð 2&K)1;=9>9(B;=(B(B&M0)3'3BÿAN59'— :T?Ý&)!"70$'[!&):F(=,G9>0t$'9'0:<;=0c9>;=2&&TM$>DA036:Z;=&)2&F:!$>;=2"&c9'(6Sm(=8!& 9Lÿ"0N )3
8!36369';B%"#%&)(BSm&‚8!949'3
 ‘9>3B0ØV9>(&G3B7)8!9>:m;B9Ë9'$>8%&)$'"K:IŠ Œ b £ƒ “ké
~¬‘9>!(B9>3B9>:m;=&)(9':Z2&G(B9>$>;&T(B9'&)I"03L3B"78!9>:<;=9'3$>0:/å68!:<;=0)3'Š
\ &<]¢æ ŒŸ P ‘ ¸ Œ hQj ¹4Œ js¾ ¨ § ÛAç
\ Xv]Ÿæ ŒŸ P ‘ ¸ 2óõ£E£ z% ƒ ” ª ñ ç
\ $~]Ÿæ ŒŸ P ‘ ¸ ¾ Œ >b Œ j Û ¯©Û Œ b ® ç
\ Dv]Ÿæ ŒŸ P ‘ ¸ Œ h j ½ b¦¾ Œ žeÛAç
E»A‘9>3B0ØV9>(&)3L:A9'$'8!&)$'"0:!9'3LWš&)3L9'$>8%&)$>0:!9>33B7)8!9>:m;B9'3>Š
\ &<] Œ j ½ ¯µ®J¸ ¾
\ Xv] Oñ Œ b ½ >b ½ j Œ ª é Œ b ®
\ $~] Œ h j Œ j é “ Œ b¦¾ Œ j ½
\ Dv] Œ j ® b Œ jsè “ÅÛ
\ 9~] Œ j Œ § ¾
¿ ­n(B8!9>XÍ9HSm8!9)Š
\ &<] Œ j Œ ö ž ² Œ b Œ ö ž ?¡ Œ hQj Œ hö ž h
–
\ Xv] Œ b  ¯›h ” ² Œ be¼ ž¤h ” ²  br¼ ¯›h ” ¡ Œ b  be¼ ž
\ $~] ÿ`md5juf ¯ ÿ`Hjuf ÿd b f ÿd*j ‹ `  d  f  P ‘
EÆA$E‰c&)0D!3L&!"8A:!:m36;=;B&)0:<3;=Ïq9Ëü?W´+Ñ×0(>3BŠ 9ËF8!9>V)9':3B0XA(B9‚8!:š36109iå69‚(69E&)ÍD!9‚0DA0™Sm8!9Ë3B8š+03B"$'"K:-9>36;&™D!&)D%&™9':
Œ ¢“ ½ü h üpbj ®® Œ Ÿ“ ü h üib h ®
‰c&-9>¬U;BO9'N (61":%&)(9'Ž0-"03:<;=9>(6V4&)"03LD!9;=9>1+0T%&)(B&"03$'8%&)"9'32&GD!"36;&4:!$'&9>:m;B(B9HϳWZÑ 9'3:Aà|9>(B"0(
EÌAD!99Ë3=9'&43o;XÍ&)93MSm&)8!I:9m[!&)IX$>9+'00™9':ZX!&)9'(BtD!"9':!&)36(;=&)9>:<I:;=m9Ë[!üQ$'"9V'0G"9':!D!99D%$'"&49'D%(o;=&0T+,40;B(>0Š 10F$'0:%&)(o; "$'8!&)3 &™D!3o;&):A$'2&!(B09'DA0
®~¨ z%ƒ · ü h juñ‚• ®~¨ z%ƒ · üIb ®)ý ¾‚• ®~¨ z%ƒl”
‰Vc9>0(B:!"#!DA$E9M&)(&)Sm3±8!%9H&)(o2&;™"$'D!8!"36&);&43±:!%$'&)(o&G;=9>&):1:<;=D!9'9>(6%(0B(L9>Í369E0&T36019'9>:T:!ü 0(L“ÅSm¨ 8!O9FNp­p¾‚&)• (=®~&¨ Sm8!·J9ÿN?9'%9—~˜*.3+9@9'.A(6Ø;=09'360T:<;=9'0t93B9'.&H+9@9'.(6";=0)9'3B:<0;=3B0 9D!9>XÍ9
z%ƒ
ˆ4ÎA­n(B0X%&4(Sm8!94Š
\ &<] ª ‹ 
\ Xv] ª ¾ ’ ‹ ª Û! 
ˆU‰c9'03o;=(=&4(+0(L":!D!8!$>K:š&)3L!(B0)Í036$>0:!9>3L3B"78!9>:<;=9'3>Š
\ &<]_^oj ® goh ’/z%ƒ “ j ®‹ 
\ Xv] ® b ½ b¦èb¦ñbì•~•~•~bq^a¾ šj ® g “ Íh ‹ 
\ $~] Œ ƒ b Œ h bk•~•~•Eb Œ ’ ¯ Œ ƒ >b Œ h >bk•~•~•Eb Œ ’ ‹ 
\ Dv]Z¾ ’ § ‹ 
\ 9~]š3B Œ¢§ j ® W  q¡ ^ ® b Œ g ’ ª ® b Œ
\ à=] ½ Ùh
b É b é 9'3D!ØV"3B"X!9‚+0(» ‹ 
\ 7m]šû;B"ÒE&):AD!0Ú9'(69'3B8A";&4D!0r&):<;=9'(60(š03o;=(=&4(šSU8A9 9>HA(B0UD!8!$>;B0eDA9_;B(B9>3Y:m[!9'(603:%&4;=8A(=&)"9'3
$'0:A3B9'$>8A;=ØV039'3D!ØVU3B"X!9cÍ0(L369'"3'
"!
#
%$
'&
%$
)(+*
(
-,/.
(
0(+*
( -,1.
(
( -,/.
2(
( -,/.
!
( -,1.
(
0( -,/.
(
(
(
3(
( 4,1.

( -,/.