a) \(3^{x-1}+3x+3^{x+1}=1053\)

\(=3^x:3+3^x+3^x.3=1053\)

\(=3^x.\dfrac{1}{3}+1+3=1053\)

\(=3^x.\dfrac{13}{5}=1053\)

\(=3^x=243\)

\(\Rightarrow x=5\)

Vậy \(x=5\)

a, \(5-\left(\frac{a}{b}+\frac{1}{2}\right)=2\frac{1}{3}\)   =>  \(\frac{a}{b}+\frac{1}{2}=5-2\frac{1}{3}\) =>  \(\frac{a}{b}+\frac{1}{2}=\frac{8}{3}\)  => \(\frac{a}{b}=\frac{8}{3}-\frac{1}{2}\) =>  \(\frac{a}{b}=\frac{13}{6}\)

b, \((\frac{3}{4}+2\frac{1}{2}):\frac{3}{5-3}=\left(\frac{3}{4}+\frac{5}{4}\right):\frac{3}{5}-1=\frac{9}{4}:\frac{-2}{5}=\frac{-45}{8}\)

a, 5-(\(\frac{a}{b}\)+\(\frac{1}{2}\))=2\(\frac{1}{3}\)

<=>5-\(\frac{a}{b}-\frac{1}{2}\)=\(\frac{7}{3}\)

<=>\(\frac{a}{b}=5-\frac{1}{2}-\frac{7}{3}\)

<=>\(\frac{a}{b}=\frac{13}{6}\)

b,(\(\frac{3}{4}\)+2\(\frac{1}{2}\)):\(\frac{3}{5}\)-3

=(\(\frac{3}{4}\)+\(\frac{5}{2}\)).\(\frac{5}{3}\)-3

=\(\frac{23}{4}\).\(\frac{5}{3}\)-3

=\(\frac{115}{12}\)-3

=\(\frac{115-36}{12}\)

=\(\frac{79}{12}\)

x = 2/3

a: \(A=1+\frac15+\frac{1}{25}+\cdots+\frac{1}{78125}\)

=>\(A=1+\frac15+\frac{1}{5^2}+\cdots+\frac{1}{5^7}\)

=>\(5\times A=5+1+\frac15+\cdots+\frac{1}{5^6}\)

=>\(5\times A-A=5+1+\frac15+\cdots+\frac{1}{5^6}-1-\frac15-\cdots-\frac{1}{5^7}\)

=>\(4\times A=5-\frac{1}{5^7}=\frac{5^8-1}{5^7}\)

=>\(A=\frac{5^8-1}{4\times5^7}\)

b:Sửa đề: \(B=\frac13+\frac{1}{12}+\cdots+\frac{1}{49152}\)

=>\(B=\frac13+\frac{1}{3\times4}+\frac{1}{3\times4^2}+\cdots+\frac{1}{3\times4^7}\)

=>\(4\times B=\frac43+\frac13+\frac{1}{3\times4}+\cdots+\frac{1}{3\times4^6}\)

=>\(4\times B-B=\frac43+\frac13+\frac{1}{3\times4}+\cdots+\frac{1}{3\times4^6}-\frac13-\frac{1}{3\times4}-\frac{1}{3\times4^2}-\cdots-\frac{1}{3\times4^7}\)

=>\(3\times B=\frac43-\frac{1}{3\times4^7}=\frac{4^8-1}{3\times4^7}\)

=>\(B=\frac{4^8-1}{9\times4^7}\)

c: \(C=\frac53+\frac56+\frac{5}{12}+\frac{5}{24}+\cdots+\frac{5}{192}+\frac{5}{384}\)

=>\(2\times C=\frac{10}{3}+\frac53+\frac56+\cdots+\frac{5}{96}+\frac{5}{192}\)

=>\(2\times C-C=\frac{10}{3}+\frac53+\frac56+\cdots+\frac{5}{96}+\frac{5}{192}-\frac53-\frac56-\cdots-\frac{5}{192}-\frac{5}{384}\)

=>\(C=\frac{10}{3}-\frac{5}{384}=\frac{1280}{384}-\frac{5}{384}=\frac{1275}{384}\)

a; \(\dfrac{a}{b}\) + \(\dfrac{5}{6}\) = 1 - \(\dfrac{1}{8}\)

   \(\dfrac{a}{b}\) + \(\dfrac{5}{6}\) =  \(\dfrac{7}{8}\)

   \(\dfrac{a}{b}\)        = \(\dfrac{7}{8}-\dfrac{5}{6}\)

     \(\dfrac{a}{b}=\) \(\dfrac{21}{24}\) - \(\dfrac{20}{24}\)

         \(\dfrac{a}{b}=\dfrac{1}{24}\)

b; \(\dfrac{5}{8}-\dfrac{a}{b}\) = \(\dfrac{1}{4}+\dfrac{1}{6}\)

    \(\dfrac{5}{8}-\dfrac{a}{b}\) = \(\dfrac{3}{12}+\dfrac{2}{12}\)

    \(\dfrac{5}{8}-\) \(\dfrac{a}{b}\) = \(\dfrac{5}{12}\)

             \(\dfrac{a}{b}\) = \(\dfrac{5}{8}-\dfrac{5}{12}\)

              \(\dfrac{a}{b}\) = \(\dfrac{15}{24}\) - \(\dfrac{10}{24}\)

                \(\dfrac{a}{b}\) = \(\dfrac{5}{24}\)

c; \(\dfrac{5}{6}\) - \(\dfrac{1}{4}\) - \(\dfrac{a}{b}\) = \(\dfrac{1}{2}\) 

   \(\dfrac{10}{12}-\dfrac{3}{12}\) - \(\dfrac{a}{b}\) = \(\dfrac{1}{2}\)

    \(\dfrac{7}{12}\) - \(\dfrac{a}{b}\) = \(\dfrac{1}{2}\)

                \(\dfrac{a}{b}\) = \(\dfrac{7}{12}\) - \(\dfrac{1}{2}\)

                \(\dfrac{a}{b}\) = \(\dfrac{7}{12}-\dfrac{6}{12}\)

                   \(\dfrac{a}{b}=\dfrac{1}{12}\) 

a) 2013 + 2013 + 2013 + 2013 + 2013 - 2013 x 4 

= 2013 x 5 - 2013 x 4

= 2013 x ( 5 - 4 )

= 2013 x 1

= 2013

b)55 - 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5

= 50 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5

= 5 x 10 + 5 x 10

= 5 x ( 10 + 10 )

= 5 x 20 = 100

c) 9999 - 999 + 999 + 999 + 999 + 999

= 9000 + 999 + 999 + 999 + 999

= 9 x 1000 + 9 x 111 x 4 

= 9 x 1000 + 9 x 444

= 9 x ( 1000 + 444 )

= 9 x 1444

=    12 996

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giúp minh đi mấy mem: rút gọn A= \(\frac{\left(a+b+c\right)^5-a^5-b^5-c^5}{\left(a+b+c\right)^3-a^3-b^3-c^3}\)