To identify any points of discontinuity in the rational function
\[ f(x) = \frac{x^2 + 2x - 3}{x + 3}, \]
we start by factoring the numerator.
The numerator \(x^2 + 2x - 3\) can be factored as follows:
- We need to find two numbers that multiply to \(-3\) and add to \(2\). The numbers \(3\) and \(-1\) fit this requirement.
- Thus, we have:
\[ x^2 + 2x - 3 = (x + 3)(x - 1). \]
Now, substituting back into the function gives us:
\[ f(x) = \frac{(x + 3)(x - 1)}{x + 3}. \]
Here, we can see that the term \(x + 3\) appears in both the numerator and the denominator. Therefore, we can simplify the function (for \(x \neq -3\)) to:
\[ f(x) = x - 1, \quad \text{for } x \neq -3. \]
However, there is a point of discontinuity at \(x = -3\) because the function is undefined there (the denominator equals zero).
Thus, we can fill in the blanks:
The point of discontinuity is located at -3 because the factor x + 3 is in the numerator and denominator.