How do I solve x-6/x-5=x-5/x-4 and get a solution set

Assuming that we have

[x-6] / [x-5]=[x-5] / [x-4]        ..... cross-multiply

[x - 6] [ x - 4]  = [x - 5] [x - 5]     simplify

x^2 - 10x + 24  = x^2 - 10x + 25        subtract  [ x^2 - 10x ]  from both sides

24  = 25    and this is impossible.....so.....no solutions exist........!!!!

x = { }        [the empty set]