My workings:
(x-3)/(x-1) = (x-4)/(x-5)
(x-3)(x-5) = (x-4)(x-1)
x^2 -8x + 15 = x^2 -5x +4
-8x + 11 = -5x
11 = 3x
x = 11/3
FWIW, wolfram alpha agrees with me.
You started with
which is not the same as
x - 3/x - 1 = x - 4/x - 5
, the equation in the submission.
My workings:
(x-3)/(x-1) = (x-4)/(x-5)
(x-3)(x-5) = (x-4)(x-1)
x^2 -8x + 15 = x^2 -5x +4
-8x + 11 = -5x
11 = 3x
x = 11/3
FWIW, wolfram alpha agrees with me.