Đáp án + Giải thích các bước giải:
`a)` `12-6x = 4(2x + 3)` $\\$ `<=> 12-6x=8x+12 <=> 12 - 6x - 8x - 12 = 0` $\\$ `<=> -14x = 0 <=> x = 0`
Vậy `S = {0}`
`b)` `(2x + 3)/2= (4x-2)/3` $\\$ `<=>[3(2x+3)]/6=[2(4x-2)]/6` $\\$ `=> 3(2x + 3) = 2(4x - 2)` $\\$ `<=> 6x + 9 = 8x - 4 <=> 6x - 8x = -4 - 9` $\\$ `<=> -2x = -13 <=> x = 13/2`
Vậy `S = {13/2}`
`c)` `|2x-5|=x+1(**)`
Ta có : `|2x - 5| = 2x - 5` khi `2x - 5 >= 0 <=> x >= 5/2`
PT (*) trở thành : `2x- 5 = x + 1 <=> 2x-x=1+5<=>x=6(TMĐK)`
`|2x - 5| = -(2x - 5)` khi `2x - 5 < 0 <=> x < 5/2`
PT (*) trở thành : `-(2x - 5) = x + 1 <=>-2x+5=x+1` $\\$ `<=> -2x - x = 1 - 5<=>-3x=-4<=>x=4/3(TMĐK)`
Vậy `S = {6; 4/3}`
`d)` `(2x - 4)/(x^2 - 25)=2/(x+5)+3/(x-5)(ĐKXĐ : x ne pm 5)` $\\$ `<=> (2x-4)/[(x-5)(x+5)]=[2(x-5)+3(x+5)]/[(x-5)(x+5)]` $\\$ `=> 2x - 4 = 2(x - 5) + 3(x + 5)` $\\$ `<=> 2x - 4 = 2x - 10 + 3x + 15` $\\$ `<=> 2x - 4 - 2x + 10 - 3x - 15 = 0` $\\$ `<=> -3x - 9 = 0 <=> x = -3(TMĐK)`
Vậy `S = {-3}`
