ĐKXĐ : \(x\ne\dfrac{3}{2}\)
\(\Leftrightarrow\dfrac{2}{9-6x}+\dfrac{2}{2x-3}=3-\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{41}{10}\)
\(\Leftrightarrow\dfrac{\dfrac{2}{-3}}{2x-3}+\dfrac{2}{2x-3}=\dfrac{41}{10}\)
\(\Leftrightarrow\left(\dfrac{1}{2x-3}\right)\left(-\dfrac{2}{3}+2\right)=\dfrac{41}{10}\)
\(\Leftrightarrow\dfrac{1}{2x-3}=\dfrac{123}{40}\)
\(\Leftrightarrow2x-3=\dfrac{40}{123}\)
\(\Leftrightarrow x=\dfrac{409}{246}\) ( TM )
Vậy ...
`3-2/(2x-3)=2/5+2/(9-6x)-3/2(x ne 3/2)`
`<=>3+3/2-2/5=2/(9-6x)-2/(2x-3)`
`<=>41/10=-2/(6x-9)+2/(2x-3)`
`<=>41/10=-2/(3(2x-3))+2/(2x-3)`
`<=>41/10=4/(3(2x-3)`
`<=>2x-3=40/123`
`<=>2x=409/123`
`<=>x=409/246`
Ta có: \(3-\dfrac{2}{2x-3}=\dfrac{2}{5}+\dfrac{2}{9-6x}-\dfrac{3}{2}\)
\(\Leftrightarrow\dfrac{3\left(2x-3\right)-2}{2x-3}=\dfrac{2}{5}-\dfrac{2}{6x-9}-\dfrac{3}{2}\)
\(\Leftrightarrow\dfrac{9\left(2x-3\right)-6}{3\left(2x-3\right)}=\dfrac{4}{10}-\dfrac{15}{10}-\dfrac{2}{3\left(2x-3\right)}\)
\(\Leftrightarrow\dfrac{18x-27-6}{6x-9}+\dfrac{2}{6x-9}=\dfrac{-11}{10}\)
\(\Leftrightarrow\dfrac{18x-31}{6x-9}=\dfrac{-11}{10}\)
\(\Leftrightarrow180x-310=-11\left(6x-9\right)\)
\(\Leftrightarrow180x-310+66x-99=0\)
\(\Leftrightarrow246x=409\)
hay \(x=\dfrac{409}{246}\)
