Is it true that (x^2–3x+2)/(x –1) = x – 2, for all values of x? justify your answer.

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