x = 5    y = 36

  ( 18 / 21 + 3 / 21 ) + ( 19 / 32 + 13 / 32 ) + ( 75 / 100 + 1 / 4 )

= 1 + 1 + 1 = 3

2008/2009 >  2010/2011 ; 1999/2001 < 12/11 ;2007/2006>  2006/2007 ; 101/100 >100/101

1. 

    x = 5

    y = 36

2.

  ( 18 / 21 + 3 / 21 ) + ( 19 / 32 + 13 / 32 ) + ( 75 / 100 + 1 / 4 ) = 1 + 1 + 1 = 3

3.

   >     ;    <       ;    >        ;        >

  x = 5    y = 36

  ( 18 / 21 + 3 / 21 ) + ( 19 / 32 + 13 / 32 ) + ( 75 / 100 + 1 / 4 )

= 1 + 1 + 1 = 3

2008/2009 >  2010/2011 ; 1999/2001 < 12/11 ;2007/2006>  2006/2007 ; 101/100 >100/101

a, A<B

b, A>B

       hok tốt

a.A

b.A>B

bạn trình bày hẳn ra

Đây nhá:

A=\(\frac{2009^{20}+9}{2009^{20}-1}=\frac{2009^{20}-1+10}{2009^{20}-1}=1+\frac{10}{2009^{20}-1}\)

B bạn tự làm như trên sẽ ra:

\(B=1+\frac{10}{2009^{19}-1}\) 

Ta có: \(\frac{10}{2009^{20}-1}< \frac{10}{2009^{19}-1}\)

\(\Rightarrow\)A<B

mai mình thi rồi, các bạn giúp mình với

Chờ tí

Câu 4: 

d) Ta có: \(\dfrac{-2}{17}+\dfrac{3}{19}+\dfrac{-15}{17}+\dfrac{16}{19}+\dfrac{5}{6}\)

\(=\left(-\dfrac{2}{17}-\dfrac{15}{17}\right)+\left(\dfrac{3}{19}+\dfrac{16}{19}\right)+\dfrac{5}{6}\)

\(=-1+1+\dfrac{5}{6}=\dfrac{5}{6}\)

Câu 3:

a) \(\dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}\)

\(\dfrac{-16}{20}=\dfrac{-16:4}{20:4}=\dfrac{-4}{5}\)

b) \(\dfrac{21}{105}=\dfrac{21:21}{105:21}=\dfrac{1}{5}\)

\(\dfrac{35}{150}=\dfrac{35:5}{150:5}=\dfrac{7}{30}\)

Câu 4: 

a) \(\dfrac{3}{10}+\dfrac{5}{10}=\dfrac{3+5}{10}=\dfrac{8}{10}=\dfrac{4}{5}\)

b) Ta có: \(\left(-27\right)\cdot36+64\cdot\left(-27\right)+23\cdot\left(-100\right)\)

\(=\left(-27\right)\cdot\left(64+36\right)+23\cdot\left(-100\right)\)

\(=-27\cdot100-23\cdot100\)

\(=100\left(-27-23\right)\)

\(=-50\cdot100=-5000\)

c) \(\dfrac{5}{8}+\dfrac{3}{12}=\dfrac{15}{24}+\dfrac{6}{24}=\dfrac{21}{24}=\dfrac{7}{8}\)

d) Ta có: \(\dfrac{-2}{17}+\dfrac{3}{19}+\dfrac{-15}{17}+\dfrac{16}{19}+\dfrac{5}{6}\)

\(=\left(-\dfrac{2}{17}+\dfrac{-15}{17}\right)+\left(\dfrac{3}{19}+\dfrac{16}{19}\right)+\dfrac{5}{6}\)

\(=-1+1+\dfrac{5}{6}\)

\(=\dfrac{5}{6}\)

\(B=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)...\left(1-\frac{1}{81}\right)\left(1-\frac{1}{100}\right)\)

\(B=\frac{3}{4}\cdot\frac{8}{9}\cdot...\cdot\frac{80}{81}\cdot\frac{99}{100}\)

\(B=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot...\cdot\frac{8.10}{9.9}\cdot\frac{9.11}{10.10}\)

\(B=\frac{\left(1\cdot2\cdot...\cdot8\cdot9\right).\left(3\cdot4\cdot...\cdot10\cdot11\right)}{\left(2\cdot3\cdot..\cdot9\cdot10\right).\left(2\cdot3\cdot...\cdot9\cdot10\right)}\)

\(B=\frac{1\cdot2\cdot...\cdot8\cdot9}{2\cdot3\cdot...\cdot9\cdot10}\cdot\frac{3\cdot4\cdot...\cdot10\cdot11}{2\cdot3\cdot...\cdot9\cdot10}\)

\(B=\frac{1}{10}\cdot\frac{11}{2}=\frac{11}{20}\)

Vì 20 < 21 nên 11/20 > 11/21

Vậy ..... 

bạn vào link này nè:https://olm.vn/hoi-dap/question/980572.html

\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)\)

\(A=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{18}{19}\cdot\frac{19}{20}\)

\(A=\frac{1}{20}\)

Vì 20 < 21 nên 1/20 > 1/21 

Vậy ............

Ta có:

\(A=\frac{19^{20}+5}{19^{20}-8}=\frac{19^{20}-8+13}{19^{20}-8}=1+\frac{13}{19^{20}-8}\)

\(B=\frac{19^{21}+6}{19^{21}-7}=\frac{19^{21}-7+13}{19^{21}-7}=1+\frac{13}{19^{21}-7}\)

Vì \(19^{20}-8< 19^{21}-7\Rightarrow\frac{13}{19^{20}-8}>\frac{13}{19^{21}-7}\)

\(\Rightarrow A>B\)

A =B NHA ! maivananh

ĐỀU = 1 CẢ . 

Ta có : \(A=\frac{19^{20}+5}{19^{20}-8}=\frac{19^{20}-8+13}{19^{20}-8}=\frac{19^{20}-8}{19^{20}-8}+\frac{13}{19^{20}-8}=1+\frac{13}{19^{20}-8}\)

          \(B=\frac{19^{21}+6}{19^{21}-7}=\frac{19^{21}-7+13}{19^{21}-7}=\frac{19^{21}-7}{19^{21}-1}+\frac{13}{19^{21}-7}=1+\frac{13}{19^{21}-7}\)

Mà : \(\frac{13}{19^{20}-8}< \frac{13}{19^{21}-7}\)

Nên : \(A< B\)

19A=19²⁰¹⁰+19/19²⁰¹⁰+1=19²⁰¹⁰+1+18/19²⁰¹⁰+1=19²⁰¹⁰+1/19²⁰¹⁰+1+18/19²⁰¹⁰+1=1+18/19²⁰¹⁰

19B=19²⁰⁰⁹+19/19²⁰⁰⁹+1=19²⁰⁰⁹+1+18/19²⁰⁰⁹+1=19²⁰⁰⁹+1/19²⁰⁰⁹+1+18/19²⁰⁰⁹+1=1+18/19²⁰⁰⁹

^{Vậy A<B}

^{Xin lỗi mình chịu câu trên}

Ta có A=\(\frac{19^{2009}+1}{19^{2010}+1}\)                                    Ta có:B=\(\frac{19^{2008}+1}{19^{2009}+1}\)

                                                                               19B=\(\frac{19^{2009}+19}{19^{2009}+1}\)

      19A=\(\frac{19^{2010}+19}{19^{2010}+1}\)                                       19B=\(\frac{19^{2009}+1+18}{19^{2009}+1}\)

      19A=\(\frac{19^{2010}+1+18}{19^{2010}+1}\)                                19B=\(1+\frac{18}{19^{2009}+1}\)

      19A=\(1+\frac{18}{19^{2010}+1}\)

                         Vì \(\frac{18}{19^{2010}+1}< \frac{18}{19^{2009}+1}\)nên \(19A< 19B\)

                          \(\Leftrightarrow A< B\)

                            Vậy\(A< B\)

\(\frac{19^{2008}+1}{19^{2009+1}}< \frac{19^{2008}+1+18}{19^{2009+1}+18}=\frac{19^{2008}+19}{19^{2009}+19}=\frac{19\left(19^{2007}+1\right)}{19\left(19^{2008}+1\right)}=\frac{\left(19^{2007}+1\right)}{\left(19^{2008}+1\right)}=>\frac{19^{2008}+1}{19^{2009+1}}< \frac{\left(19^{2007}+1\right)}{\left(19^{2008}+1\right)}\)