Đáp án:

`a, x=1/4`

`b,x=3`

Giải thích các bước giải:

`a, (9-4x)/(9x^2-1) =3/(3x+1) -5/(1-3x)`       đk `x \ne 1/3 ; x \ne -1/3`

`(9-4x)/((3x+1)(3x-1)) =3/(3x+1) +5/(3x-1)`

`(9-4x)/((3x+1)(3x-1)) =(3(3x-1))/((3x+1)(3x-1)) +(5(3x+1))/((3x+1)(3x-1))`

`9-4x =3(3x-1) +5(3x+1)`

`9-4x = 9x -3 +15x +5`

`9-4x - 9x +3 -15x -5 =0`

`-28x +7=0`

`-28x=-7`

`x=1/4 (tm)`

Vậy pt có nghiệm `x=1/4`

`b, (2x-3)/(x+1) + (x^2 -5x +22)/(x^2 -2x -3) =(3x-5)/(x-3) `     đk `x \ne -1 ; x \ne 3`

`(2x-3)/(x+1) + (x^2 -5x +22)/(x^2 -3x+x -3) =(3x-5)/(x-3)`

`(2x-3)/(x+1) + (x^2 -5x +22)/((x-3)(x+1)) =(3x-5)/(x-3)`

`((2x-3)(x-3))/((x-3)(x+1))+ (x^2 -5x +22)/((x-3)(x+1)) =((3x-5)(x+1))/((x-3)(x+1))`

`(2x-3)(x-3)+ x^2 -5x +22 =(3x-5)(x+1)`

`2x^2 -6x -3x +9 + x^2 -5x +22 = 3x^2 +3x -5x -5`

`2x^2 -6x -3x +9 + x^2 -5x +22 - 3x^2 -3x +5x +5 =0`

` -12x  +36 =0`

`-12x=-36`

`x=3 (tm)`

Vậy pt có nghiệm `x=3`