I do not think that this has a solution, is that correct?
(y-3)/(y-6)=3/(y-6)
It does have a solution, but it is a "limiting case" of the equation you have written. Since the denominators on both sides are the same, the numerators must be equal. Therefore
y-3 = 3
y = 6
The trouble is that the fractions are undefined when y = 6. In the limiting case as y -> 6, the equation becomes satisfied with increasing accuracy.