Are they the same?

The graphs of ${\color{darkred} {y=\dfrac{x^2-9}{x-3}}}$ and ${\color{#456461}{y=x+3}}$ are shown below, respectively.

$y=\dfrac{x^2-9}{x-3}$ simplifies to $y=x+3$ . However, when graphed, the value of $\dfrac{x^2-9}{x-3}$ when $x=3$ is undefined, since it results in division by zero. Therefore the answer is $\boxed{\text{No}}$ , they are not the same.