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