Question

2x/x-5 + 1/x-1=0

Answer 1

I am sure you meant:

2x/(x-5) + 1/(x-1) = 0

multiply each of the three terms by (x-5)(x-1) , the LCD

2x(x-1) + 1(x-5) = 0
2x^2 - 2x + x - 5 = 0
2x^2 - x - 5 = 0
x = (1 ± √41)/4

the way you have it, it would be
2 - 5 + 1/x - 1 0
1/x = 4
x = 1/4