`( 3 3/4 + 5 3/8)/(x-2) + 6/(3x -6) = 5 2/3 + 1 3/4`
`(15/4 + 43/8)/(x-2) + 6/(3(x-2)) = 17/3 + 7/4`
`(30/8 + 43/8)/(x-2) + 2/(x-2) = 68/12 + 21/12`
`(73/8 + 2)/(x-2) = 89/12`
`(89/8)/(x-2) = 89/12`
`x-2 = (89/8)/(89/12)`
`x-2=3/2`
`x = 3/2 + 2`
`x= 7/2`
\(\dfrac{3\dfrac{3}{4}+5\dfrac{3}{8}}{x-2}+\dfrac{6}{3\times x-6}=5\dfrac{2}{3}+1\dfrac{3}{4}\)
\(\Rightarrow\dfrac{\dfrac{15}{4}+\dfrac{43}{8}}{x-2}+\dfrac{6}{3\left(x-2\right)}=\dfrac{17}{3}+\dfrac{7}{4}\)
\(\Rightarrow\dfrac{\dfrac{73}{8}+2}{x-2}=\dfrac{89}{12}\)
\(\Rightarrow\dfrac{\dfrac{89}{8}}{x-2}=\dfrac{89}{12}\)
\(\Rightarrow89\left(x-2\right)=\dfrac{89}{8}.12\)
\(\Rightarrow89x-178=\dfrac{267}{2}\)
\(\Rightarrow89x=\dfrac{623}{2}\)
\(\Rightarrow x=\dfrac{7}{2}\)
Vậy: \(x=\dfrac{7}{2}\)