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A

\(\dfrac{x}{2}.\left(\dfrac{3x-13}{5}\right)=\dfrac{21x}{10}\)

\(\left(\dfrac{3x-13}{5}\right)=\dfrac{21x}{10}.\dfrac{2}{x}\)

\(\dfrac{3x-13}{5}=\dfrac{21}{5}\)

3x - 13 = 21 

3x = 34

x = 34/3

`a, 3-(x+5/7 )=9/21`

`=>x+5/7= 3-9/21`

`=>x+5/7= 63/21-9/21`

`=>x+5/7= 54/21`

`=>x= 54/21-5/7`

`=>x= 54/21 - 15/21`

`=>x= 39/21`

`=>x= 13/7`

`b, x/2+ x/5 = 17/10`

`=> (5x)/10 + (2x)/10=17/10`

`=> 7x/10=17/10`

`=> 7x.10=10.17`

`=>7x.10=170`

`=>7x=170:10`

`=>7x=17`

`=>x=17/7`

`c, 1/2x + 1/3 -1= 3 1/3`

`=>  1/2x + 1/3 -1=  10/3`

`=>   1/2x + 1/3=10/3+1`

`=>   1/2x + 1/3=10/3 + 3/3`

`=>   1/2x + 1/3=13/3`

`=>1/2 x= 13/3 -1/3`

`=> 1/2x= 12/3`

`=> 1/2x= 4`

`=>x= 4 :1/2`

`=>x= 4 xx 2`

`=>x=8`

\(a,3-\left(x+\dfrac{5}{7}\right)=\dfrac{9}{21}\\ x+\dfrac{5}{7}=3-\dfrac{9}{21}\\ x+\dfrac{5}{7}=\dfrac{18}{7}\\ x=\dfrac{18}{7}-\dfrac{5}{7}\\ x=\dfrac{13}{7}\\ b,\dfrac{x}{2}+\dfrac{x}{5}=\dfrac{17}{10}\\ \dfrac{5x}{10}+\dfrac{2x}{10}=\dfrac{17}{10}\\ \dfrac{7x}{10}=\dfrac{17}{10}\\ 7x=17\\ x=\dfrac{17}{7}\\ c,\dfrac{1}{2}x+\dfrac{1}{3}-1=3\dfrac{1}{3}\\ \dfrac{1}{2}x+\dfrac{1}{3}-1=\dfrac{10}{3}\\ \dfrac{1}{2}x+\dfrac{1}{3}=\dfrac{10}{3}+1\\ \dfrac{1}{2}x+\dfrac{1}{3}=\dfrac{13}{3}\\ \dfrac{1}{2}x=\dfrac{13}{3}-\dfrac{1}{3}\\ \dfrac{1}{2}x=4\\ x=4:\dfrac{1}{2}\\ x=10\)

\(\text{a)}\dfrac{-3}{5}-x=\dfrac{21}{10}\)

             \(x=\dfrac{-3}{5}-\dfrac{21}{10}=\dfrac{-27}{10}\)

\(\text{b)}x:\dfrac{2}{9}=\dfrac{9}{2}\)

   \(x\)        \(=\dfrac{9}{2}.\dfrac{2}{9}=1\)

\(\text{c) }\dfrac{x}{9}=\dfrac{5}{3}\)

\(\Rightarrow x=\dfrac{9.5}{3}=15\)

\(\text{d)}x:\left(\dfrac{2}{5}\right)^3=\left(\dfrac{5}{2}\right)^3\)

   \(x:\dfrac{8}{125}=\dfrac{125}{8}\)

   \(x\)           \(=\dfrac{125}{8}.\dfrac{8}{125}=1\)

a,     \(\dfrac{3}{7}\)\(x\)- \(\dfrac{2}{3}\)\(x\)    = \(\dfrac{10}{21}\)

    (\(\dfrac{3}{7}\) - \(\dfrac{2}{3}\)) \(\times\) \(x\)  =  \(\dfrac{10}{21}\)

     - \(\dfrac{5}{21}\) \(\times\) \(x\)      = \(\dfrac{10}{21}\)

                 \(x\)      = \(\dfrac{10}{21}\) : (-\(\dfrac{5}{21}\))

                 \(x\)      = -2 

b, \(\dfrac{7}{35}\) : (\(x-\dfrac{1}{3}\)) = - \(\dfrac{2}{25}\)

            \(x\) - \(\dfrac{1}{3}\)    =  \(\dfrac{7}{35}\) : (- \(\dfrac{2}{25}\))

             \(x\) - \(\dfrac{1}{3}\) = - \(\dfrac{5}{2}\)

             \(x\)       =  - \(\dfrac{5}{2}\) + \(\dfrac{1}{3}\)

              \(x\)      = - \(\dfrac{13}{6}\)

c, 3.(\(x\) - \(\dfrac{1}{2}\)) - 5.(\(x\) + \(\dfrac{3}{5}\)) = - \(x\)+ \(\dfrac{1}{5}\)

     3\(x\) - \(\dfrac{3}{2}\) - 5\(x\) - 3 = - \(x\) + \(\dfrac{1}{5}\)

      - \(x\) + 5\(x\) - 3\(x\) = - \(\dfrac{3}{2}\) - 3 - \(\dfrac{1}{5}\)

              \(x\)           = - \(\dfrac{47}{10}\)

\(a,\dfrac{3}{7}x-\dfrac{2}{3}x=\dfrac{10}{21}\\ \Rightarrow x\left(\dfrac{3}{7}-\dfrac{2}{3}\right)=\dfrac{10}{21}\\ \Rightarrow x.-\dfrac{5}{21}=\dfrac{10}{21}\\ \Rightarrow x=-2\\ b,\dfrac{7}{35}:\left(x-\dfrac{1}{3}\right)=-\dfrac{2}{25}\\ \Rightarrow\dfrac{1}{5}:\left(x-\dfrac{1}{3}\right)=-\dfrac{2}{25}\\ \Rightarrow x-\dfrac{1}{3}=-\dfrac{5}{2}\\ \Rightarrow x=-\dfrac{13}{6}\\ c,3.\left(x-\dfrac{1}{2}\right)-5.\left(x+\dfrac{3}{5}\right)=-x+\dfrac{1}{5}\\ \Rightarrow3x-\dfrac{3}{2}-5x+5=-x+\dfrac{1}{5}\)

\(\Rightarrow x\left(3-5\right)-\dfrac{3}{2}+5=-x+\dfrac{1}{5}\\ \Rightarrow-2x-\dfrac{13}{2}=-x+\dfrac{1}{5}\\ \Rightarrow-x-\dfrac{13}{5}=\dfrac{1}{5}\\ \Rightarrow x=\dfrac{1}{5}-\dfrac{13}{5}\\ \Rightarrow x=-\dfrac{12}{5}.\)

a,73​x−32​x=2110​⇒x(73​−32​)=2110​⇒x.−215​=2110​⇒x=−2b,357​:(x−31​)=−252​⇒51​:(x−31​)=−252​⇒x−31​=−25​⇒x=−613​c,3.(x−21​)−5.(x+53​)=−x+51​⇒3x−23​−5x+5=−x+51​

⇒�(3−5)−32+5=−�+15⇒−2�−132=−�+15⇒−�−135=15⇒�=15−135⇒�=−125.⇒x(3−5)−23​+5=−x+51​⇒−2x−213​=−x+51​⇒−x−513​=51​⇒x=51​−513​⇒x=−512​.

\(\dfrac{-3}{5}-x=\dfrac{21}{10}\)

\(x=\dfrac{-3}{5}-\dfrac{21}{10}\)

\(x=\)-\(\dfrac{27}{10}\)

\(x:\dfrac{2}{9}=\dfrac{9}{2}\)

\(x.\dfrac{9}{2}=\dfrac{9}{2}\)

\(x=\dfrac{9}{2}:\dfrac{9}{2}\)

\(x=1\)

\(\dfrac{x}{9}=\dfrac{5}{3}\)

\(x.3=5.9\)

\(x.3=45\)

\(x=45:3=15\)

\(x:\left(\dfrac{2}{5}\right)^3=\left(\dfrac{5}{2}\right)^3\)

\(x:\dfrac{8}{125}=\dfrac{125}{8}\)

\(x.\dfrac{125}{8}=\dfrac{125}{8}\)

\(x=\dfrac{125}{8}:\dfrac{125}{8}=1\)

a) 

\(\dfrac{-5}{21}+\left(\dfrac{-16}{21}+1\right)=\dfrac{-5}{21}+\dfrac{-16}{21}+1\)=\(-1+1=0\)

`(-5)/21+((-16)/21+1)`

`=(-5)/21-16/21+1`

`=-1+1=0`

`(-3)/8*1/6+3/(-8)*5/6+(-1)/16`

`=-3/8*(1/6+5/6)-10/16`

`=-3/8-10/16`

`=-6/16-10/16=-16/16=-1`

\(\dfrac{-3}{8}.\dfrac{1}{6}+\dfrac{-3}{8}.\dfrac{5}{6}+\dfrac{-10}{16}\)

=\(\dfrac{-3}{8}.\left(\dfrac{1}{6}+\dfrac{5}{6}\right)+\dfrac{-10}{16}\)

=\(\dfrac{-3}{8}+\dfrac{-5}{8}=-1\)=

98775 - 32 x 85

=98775 -2720

=96055

 67500 - 24 x 236

= 67500 -5664

=61836

 568 + 101598 : 287

= 568 +354

=922

6875 + 980 -180  

=7855 -180 

=7675

\(\dfrac{2}{5}+\dfrac{3}{10}-\dfrac{1}{2}\)

\(=\dfrac{7}{10}-\dfrac{1}{2}\)

= \(\dfrac{1}{5}\)

\(\dfrac{8}{11}+\dfrac{8}{33}x\dfrac{3}{4}\)

\(=\dfrac{8}{11}+\dfrac{2}{11}\)

\(=\dfrac{10}{11}\)

\(\dfrac{7}{9}x\dfrac{3}{14}:\dfrac{5}{8}\)

\(=\dfrac{1}{6}:\dfrac{5}{8}\)

\(=\dfrac{1}{6}x\dfrac{8}{5}\)

\(=\dfrac{8}{30}\)

\(=\dfrac{4}{15}\)

\(\dfrac{5}{12}-\dfrac{7}{32}:\dfrac{21}{16}\)

\(=\dfrac{5}{12}-\dfrac{7}{32}x\dfrac{16}{21}\)

\(=\dfrac{5}{12}-\dfrac{1}{6}\)

\(=\dfrac{5}{12}-\dfrac{2}{12}\)

\(=\dfrac{3}{12}=\dfrac{1}{4}\)

_{Tín hịu cầu kíu :>>}

\(=\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\cdot\dfrac{10-6-3-1}{30}=0\)

\(\left(\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{10}-\dfrac{1}{30}\right)\times\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\)

\(=\left(\dfrac{10}{30}-\dfrac{6}{30}-\dfrac{3}{30}-\dfrac{1}{30}\right)\times\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\)

\(=0\times\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\)

\(=0\)

a: \(x-3\left(2x-6\right)=21-\left(5x+3\right)\)

=>\(x-6x+18=21-5x-3\)

=>18=18(luôn đúng)

=>\(x\in R\)

b: \(\left(x-2\right)\left(x+2\right)-\left(x-1\right)^2=2\left(x+1\right)\)

=>\(x^2-4-x^2+2x-1=2x+2\)

=>2x-5=2x+2

=>-7=0(vô lý)

=>\(x\in\varnothing\)

c: \(\dfrac{9x+4}{6}=1-\dfrac{3x-5}{9}\)

=>\(\dfrac{3\left(9x+4\right)}{18}=\dfrac{18}{18}-\dfrac{2\left(3x-5\right)}{18}\)

=>3(9x+4)=18-2(3x-5)

=>27x+12=18-6x+10

=>27x+12=-6x+28

=>33x=16

=>\(x=\dfrac{16}{33}\left(nhận\right)\)

d: ĐKXĐ: \(x\notin\left\{2;5\right\}\)

\(\dfrac{6x+1}{x^2-7x+10}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)

=>\(\dfrac{6x+1}{\left(x-2\right)\left(x-5\right)}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)

=>\(6x+1+5\left(x-5\right)=3\left(x-2\right)\)

=>6x+1+5x-25=3x-6

=>11x-24=3x-6

=>8x=18

=>\(x=\dfrac{9}{4}\left(nhận\right)\)

a: 

=>

=>18=18(luôn đúng)

=>

b: 

=>

=>2x-5=2x+2

=>-7=0(vô lý)

=>x∈∅

c: 3(9x+4)18=1818−2(3x−5)18

=>3(9x+4)=18-2(3x-5)

=>27x+12=18-6x+10

=>27x+12=-6x+28

=>33x=16

=>

=>