Đáp án+Giải thích các bước giải:
`a)4(x+2)-1=x-5`
`⇔4x+8-1=x-5`
`⇔4x+7=x-5`
`⇔4x-x=-5-7`
`⇔3x=-12`
`⇔x=-4`
Vậy `S=\{-4\}`
`b)ĐKXĐ:x\ne -1;x\ne 2`
`2/(x+1)-1/(x-2)=(3x-11)/((x+1)(x-2))`
`⇔(2(x-2))/((x+1)(x-2))-(1(x+1))/((x-2)(x+1))=(3x-11)/((x+1)(x-2))`
`⇒2(x-2)-(x+1)=3x-11`
`⇔2x-4-x-1=3x-11`
`⇔x-5=3x-11`
`⇔3x-x=-5+11`
`⇔2x=6`
`⇔x=3(TM)`
Vậy `S=\{3\}`
`c)(x-2)(2x-1)=5(x-2)`
`⇔(x-2)(2x-1)-5(x-2)=0`
`⇔(x-2)[(2x-1)-5]=0`
`⇔(x-2)(2x-1-5)=0`
`⇔(x-2)(2x-6)=0`
\(⇔\left[ \begin{array}{l}x-2=0\\2x-6=0\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=2\\2x=6\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=2\\x=3\end{array} \right.\)
Vậy `S=\{2;3\}`
