Solve this rational equation: 3/x-1 + 8/x=3

Please help me out!! The answer said 2/3 and 4...I got 2/3 but how do you get 4. Please show steps, I've been stuck for a cool minute.

3 / (x - 1) + 8 / x = 3 ∙ ∙ ∙ ∙ ∙ ∙ ∙ multiply by lcd, which is x(x - 1)
3x + 8(x - 1) = 3x(x - 1)
3x + 8x - 8 = 3x² - 3x
0 = 3x² - 14x + 8
0 = (3x – 2)(x – 4) ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ now zero product property
3x – 2 = 0 ∙ ∙ ∙ x = 2/3
x – 4 = - ∙ ∙ ∙ ∙ x = 4

3/(x-1) + 8/x=3
3x/x(x-1)+8(x-1)/x(x-1)=3
(3x+8x-8)/x(x-1)=3
(x(x-1))*(11x-8)/(x(x-1))=3(x(x-1))
11x-8=3(x^2-x)
11x-8=3x^2-3x
0=3x^2-14x+8

Quad formula: (-(-14)+/-sqrt((-14)^2-4(3)(8)))/(2*3)
(14+/-sqrt(196-96))/ 6
(14+/-10)/6
ANSWERS: 24/6=4 and 4/6=2/3

3/(x-1) + 8/x=3
Multiply this part 3/(x-1) with x/x
3x/(x-1)x + 8/x=3
Multiply this part 8/x with (x-1)/(x-1)
3x/(x-1)x + 8(x-1)/x(x-1) = 3
3x/(x-1)x + (8x-8)/(x-1)x = 3
(3x+8x-8)/(x-1)x = 3
(11x-8)/(x-1)x = 3
11x-8 = 3 x (x-1)
11x-8 = 3x^2 -3x
0 = 3x^2 -3x -11x +8
0 = 3x^2 -14x +8
0 = (3x-2)(x-4)

3x-2 = 0
3x = 2
x = 2/3

x-4 = 0
x = 4

Multiply by x(x-1)
3x + 8(x - 1) = 3x(x - 1)
3x + 8x - 8 = 3x² - 3x
11x - 8 = 3x² - 3x
3x² - 14x + 8 = 0

Philo beat me to it (I don't want to cheat).