Simplify: $\frac{x^2-9}{x+3}$

To simplify the given algebraic expression, we can analyze the numerator and the denominator step-by-step.

The given expression is:
$\frac{x^2-9}{x+3}$

First, let's look at the numerator, which is $x^2-9$. Notice that this expression is a difference of two squares, since 9 can be written as $3^2$.
We can factor it using the difference of squares formula, $a^2-b^2=(a-b)(a+b)$:
$x^2-9=x^2-3^2=(x-3)(x+3)$

Now, we substitute this factored form back into the original expression:
$\frac{(x-3)(x+3)}{x+3}$

Assuming $x\ne -3$, we can cancel out the common factor of $x+3$ from both the numerator and the denominator:
$x-3$

Therefore, the simplified form of the expression is x – 3.