a)x-3/x-2 + x-2/x-4 = -1 b)3x + 12 = 0 c)5 + 2x = x - 5 d)2x(x - 2) + 5(x - 2) = 0 e)3x-4/2 = 4x+1/3 f)2x/x-1 - x/x+1 =1 g)2x/x-1 + 3-2x/x+2 = 6/(x-1)(x+2)

Đáp án + Giải thích các bước giải:

`b) 3x + 12 = 0 `

`<=> 3x = - 12 `

`<=> x = - 4 `

Vậy `S = { - 4 } `

`c) 5 + 2x = x - 5 `

`<=> 2x - x = - 5 - 5 `

`<=> x = - 10 `

Vậy `S = { - 10 } `

`d) 2x ( x - 2 ) + 5 ( x - 2 ) = 0 `

`<=> ( x - 2 ) ( 2x + 5 ) = 0 `

`<=> `\(\left[ \begin{array}{l}x-2=0\\2x+5=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=2\\x=-\dfrac{5}{2} \end{array} \right.\) 

Vậy `S = { 2 ; - 5/2 } `

`e) ( 3x - 4 )/2 = ( 4x + 1 )/3 `

`<=> ( 3 ( 3x - 4 ))/6 = ( 2 ( 4x + 1 ))/6 `

`=> 3 ( 3x - 4 ) = 2 ( 4x + 1 ) `

`<=> 9x - 12 = 8x + 2 `

`<=> 9x - 8x = 2 + 12 `

`<=> x = 14 `

Vậy `S = { 14 } `

`f) ( 2x )/( x - 1 ) - x/( x + 1 ) = 1 `

`<=> ( 2x ( x + 1 ))/(( x - 1 ) ( x + 1 )) - ( x ( x - 1 ))/(( x - 1 ) ( x + 1 )) = (( x - 1 ) ( x + 1 ))/(( x - 1 ) ( x + 1 ))`

`=> 2x ( x + 1 ) - x ( x - 1 ) = ( x - 1 ) ( x + 1 ) `

`<=> 2x^2 + 2x - x^2 + x = x^2 + x - x - 1 `

`<=> x^2 + 2x = x^2 - 1 `

`<=> x^2 - x^2 + 2x = - 1 `

`<=> 2x = - 1 `

`<=> x = - 1/2 `

Vậy `S = { - 1/2 } `

$\boxed{dieulinh}$