`***`Lời giải`***`
1)
a)
`\frac{2x+1}{3}-\frac{3x-2}{2}≥\frac{1}{6}+x `
`<=>\frac{2(2x+1)}{6}-\frac{3(3x-2)}{6}≥\frac{1}{6}+\frac{6x}{6} `
`<=>4x+2-(9x-6)≥1+6x`
`<=>4x+2-9x+6≥1+6x`
`<=>4x-9x-6x≥1-2-6`
`<=>-11x≥-7`
`<=>11x≤7`
`<=>x≤7/11`
Vậy `S={x`/`x≤7/11}`
b)ĐKXĐ: `xne1`
`\frac{2x+1}{x-1}<1`
`<=>\frac{2x+1}{x-1}-1<0`
`<=>\frac{2x+1-(x-1)}{x-1}<0`
`<=>\frac{2x+1-x+1}{x-1}<0`
`<=>\frac{x+2}{x-1}<0`
`<=>`\(\left[ \begin{array}{l}\begin{cases} x+2<0\\x-1>0 \end{cases}\\\begin{cases} x+2>0\\x-1<0\end{cases}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\begin{cases} x<-2\\x>1 \end{cases}(L)\\\begin{cases} x>-2\\x<1\end{cases}(N)\end{array} \right.\)
Vậy `S={x`/`-2<x<1}`
2) ĐKXĐ: `xne±1`
`A=(\frac{x+3}{x^2-1}-\frac{3}{x+1}):(1-\frac{2}{x-1})`
`=\frac{x+3-3(x-1)}{(x-1)(x+1)}:(1-\frac{2}{x-1})`
`=\frac{x+3-3x+3}{(x-1)(x+1)}:\frac{x-1-2}{x-1}`
`=\frac{-2x+6}{(x-1)(x+1)}:\frac{x-3}{x-1}`
`=\frac{-2(x-3)}{(x-1)(x+1)}:\frac{x-3}{x-1}`
`=\frac{-2(x-3)}{(x-1)(x+1)}.\frac{x-1}{x-3}`
`=\frac{-2}{x+1}`
