Bài `3.`

`1.`

`(x+2)/(x-2) - 6/(x+2) = x^2/(x^2-4)`

Đkxđ : `x ne +-2` 

`(x+2)^2/((x-2)(x+2)) - (6(x-2))/((x-2)(x+2))= x^2/((x-2)(x+2))`

`x^2 + 4x + 4 - 6x + 12 = x^2`

`x^2 + 4x + 4 - 6x + 12 - x^2 = 0`

`-2x + 16 = 0`

`-2x = -16`

`x = 8` `(tm)`

Vậy `S = {8}` .

`2.`

`x/(x+3) - (2x-1)/(3-x) = (2x^2+4x)/(x^2-9)`

Đkxđ : `x ne +- 3` 

`x/(x+3) + (2x-1)/(x-3) = (2x^2+4x)/(x^2-9)`

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

`x^2 - 3x+2x^2+6x-x-3= 2x^2+4x`

`x^2 - 3x+2x^2+6x-x-3- 2x^2-4x=0`

`x^2 - 2x - 3 = 0`

`(x-3)(x+1) = 0`

Có `x = 3` `(ktm)` và `x = -1` `(tm)`

Vậy `S = {-1}` .

`3.`

`(x-5)/(x+5) - (2x)/(x-5) = (x(x+10))/(25-x^2)`

Đkxđ : `x ne +-5` 

`(x-5)/(x+5) - (2x)/(x-5) = (-x(x+10))/(x^2-25)`

`(x-5)^2/((x-5)(x+5)) - (2x(x+5))/((x-5)(x+5)) = (-x(x+10))/((x-5)(x+5))`

`x^2-10x+25-2x^2-10x = -x^2-10x`

`x^2-10x+25-2x^2-10x +x^2+10x = 0`

`-10x + 25 = 0`

`-10x = -25`

`x = (-25)/(-10) = 5/2` `(tm)`

Vậy `S={5/2}` .

`4.`

`5/(x-3) + 4/(x+3) = (x-5)/(x^2-9)`

Đkxđ : `x ne +-3` 

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

`5x+15+4x-12=x-5`

`5x+15+4x-12-x+5=0`

`8x + 8 =  0`

`8x = -8`

`x = -1` `(tm)`

Vậy `S={-1}` .

`5.`

`(x+3)/(x-3) - (x-3)/(x+3) = 48/(9-x^2)`

Đkxđ : `x ne +-3` 

`(x+3)/(x-3) - (x-3)/(x+3) = (-48)/(x^2-9)`

`(x+3)^2/((x-3)(x+3)) - (x-3)^2/((x-3)(x+3)) = (-48)/((x-3)(x+3))`

`x^2+6x+9-x^2+6x-9 = -48`

`x^2+6x+9-x^2+6x-9 +48 = 0`

`12x + 48 = 0`

`12x = -48`

`x = -4` `(tm)`

Vậy `S = {-4}` .

`6.`

`(x-1)/(x+2) - (5x-2)/(x^2-4) = x/(x-2)`

Đkxđ : `x ne +-2` 

`((x-1)(x-2))/((x-2)(x+2)) - (5x-2)/((x-2)(x+2)) = (x(x+2))/((x-2)(x+2))`

`x^2-3x+2-5x+2=x^2+2x`

`x^2-3x+2-5x+2-x^2-2x=0`

`-10x + 4 = 0`

`-10x = -4`

`x = (-4)/(-10) = 2/5` `(tm)`

Vậy `S = {2/5}` .