The given expression is:

$\frac{x+5}{x^2 - 9}$

To simplify or analyze this expression further, we notice that the denominator $x^2 - 9$ is a difference of squares, which can be factored as:

$x^2 - 9 = (x - 3)(x + 3)$

Thus, the expression can be rewritten as:

$\frac{x+5}{(x-3)(x+3)}$

This is the simplified form of the expression. There are no common factors between the numerator and denominator, so it cannot be simplified further.

Domain Restrictions: The values of $x$ that make the denominator zero are the values where the expression is undefined. Setting the denominator equal to zero:

$(x - 3)(x + 3) = 0$

This gives $x = 3$ and $x = -3$. Therefore, the expression is undefined for $x = 3$ and $x = -3$.

Would you like further details or clarifications?

Related Questions:

1. What is the domain of the expression?
2. How do you factor more complex quadratics?
3. Can we graph this rational function and analyze its behavior?
4. How does the expression change if we add terms to the numerator?
5. What happens to the function as $x$ approaches 3 or -3?

Tip:

Always factor denominators when dealing with rational expressions, as it helps in identifying domain restrictions and simplifying the expression.