So it is clear to me that something like (x^2 - 5x+ 6)/ (x-3) simplifies to x-2

But if i now think about the function f(x) = (x^2 - 5x+ 6)/(x-3) and explores the sketch on a graph plotter , it draws a straight line x-2,

I know there is a problem at x=3 but are we saying the two things are equivalent or not?

So what is the sketch of f(x) if it is not a line?