Is $\frac {x^2 + 5x}{x} = x+5$? We are graphing functions in class and the function $f(x) = \frac {x^2 + 5x}{x}$, came up and our teacher simplified it to $x+5$ and graphed that with a hole in the function at $x=0$.
I started wondering, how in algebra can we say that $\frac {x^2 + 5x}{x} = x+5$, when the graphs of each function are not equal?
Thanks

It is indeed invalid to write "$\frac{x^2+5x}{x} = x+5$". In general, a lot of people are imprecise and never specify properly what objects they are talking about. In this case, what is $x$? Once you answer that question right, you get a true statement:

$\frac{x^2+5x}{x} = x+5$ for any real $x \ne 0$.

This means that you can plot the graph of $y = \frac{x^2+5x}{x}$ by following the graph of $y = x+5$ for all reals $x \ne 0$. For $x = 0$, of course $\frac{x^2+5x}{x}$ is undefined so we leave a hole there.
