# Thread: algebraic fractions /functions question

1. ## algebraic fractions /functions question

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?

2. ## Re: algebraic fractions /functions question

The graph of $\displaystyle y= \frac{x^2- 5x+ 6}{x- 3}$ is a "straight line with a hole in it".

$\displaystyle \frac{x^2- 5x+ 6}{x- 3}= x- 2$ for all x except x= 3. There is no value at x= 3 because when x= 3, $\displaystyle y= \frac{0}{0}$ which is "undefined".

On a "graph plotter" you don't see the "hole" because it is a single point.

3. ## Re: algebraic fractions /functions question

Thanks, i thought it must be something like this! A bit deep this stuff