`#Sad`
`a)`
`(x-3)/(x-2)+(x+2)/x = 2` `\text{(ĐKXĐ:}` `x \ne 0;` `x \ne 2)`
`⇔ (x(x-3))/(x(x-2))+((x+2)(x-2))/(x(x-2)) = (2x(x-2))/(x(x-2))`
`⇒ x^2-3x+x^2-4 = 2x-4x`
`⇔ 2x^2-3x-2x^2-4+4x = 0`
`⇔ x-4 = 0`
`⇔ x = 4` `\text{(TMĐK)}`
`\text{Vậy S=}` `{4}`
`b)`
`(x-2)((2)/(3)x-6) = 0`
`⇔` \(\left[ \begin{array}{l}x-2=0\\\dfrac{2}{3}x-6 = 0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=2\\\dfrac{2}{3}x=6\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=2\\x=9\end{array} \right.\) `\text{(TMĐK)}`
`\text{Vậy S=}` `{2; 9}`
`c)`
`(x-3)/(x-2)+(x+2)/x = 2` `\text{(ĐKXĐ:}` `x \ne 0;` `x \ne 2)`
`⇔ (x(x-3))/(x(x-2))+((x+2)(x-2))/(x(x-2)) = (2x(x-2))/(x(x-2))`
`⇒ x^2-3x+x^2-4 = 2x-4x`
`⇔ 2x^2-3x-2x^2-4+4x = 0`
`⇔ x-4 = 0`
`⇔ x = 4` `\text{(TMĐK)}`
`\text{Vậy S=}` `{4}`
`d)`
`x/(x-1)-(2x-3)/(x-1) = (2x+3)/(x^2-1)` `\text{(ĐKXĐ:}` `x \ne +- 1)`
`⇔ (x(x-1))/((x-1)(x+1))-((x+1)(2x-3))/((x-1)(x+1)) = (2x+3)/((x-1)(x+1))`
`⇒ x^2-x-2x^2+3x-2x+3 = 2x+3`
`⇔ -x^2-2x-3+3 = 0`
`⇔ -x^2-2x = 0`
`⇔ -x(x+2) = 0`
`⇔` \(\left[ \begin{array}{l}-x=0\\x+2=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=0\\x=-2\end{array} \right.\) `\text{(TMĐK)}`
`\text{Vậy S=}` `{0; -2}`
`f)`
`(x-1)/x+(x-2)/(x+1) = 2` `\text{(ĐKXĐ:}` `x \ne 0;` `x \ne -1)`
`⇔ ((x-1)(x+1))/(x(x+1))+(x(x-2))/(x(x+1)) = (2x)(x+1))/(x(x+1))`
`⇒ x^2-1+x^2-2x = 2x(x^2-1)`
`⇔ 2x^2-2x-1-2x^2-2x = 0`
`⇔ -4x + 1 = 0`
`⇔ -4x = 1`
`⇔ x = -1/4` `\text{(TMĐK)}`
`\text{Vậy S=}` `{-1/4}`
