2x/x-4 + 4/x-3 = 8/x^2-7x+12

did you notice that

x^2 - 7x + 12 = (x-4)(x-3) which happen to be denominators of the first 2 terms?
So the LCD is (x-4)(x-3)
Multiply each term by that LCD to get

2x(x-3) + 4(x-4) = 8
2x^2 + 4x - 30 = 0
x^2 + 2x - 15 = 0
(x+5)(x-3) = 0
x = -5 or x = 3
BUT x=3 would make the expression undefined,
so
x = -5