no, if x=1 then you get an undefined statement
if you want to try to simplify then
x^2-3x+2=(x-1)(x-2)
((x-1)(x-2))/(x-1)=x-2 is that true?
x-1 cancels out
x-2=x-2
true
but, the x-1 is trickey
if x=1, then the denomenator becomes 0 and the equation is undefined
undefined =x-2 is false
answer if no
but if your teacher says that it is true because of simplification tell that x=1 doesn't work