Question

where is the hole for the following function located?
$f(x)=\frac{x + 3}{(x - 4)(x + 3)}$
$\bigcirc\\ x = -3$
$\bigcirc\\ y = -3$
$\bigcirc\\ x = 3$
$\bigcirc\\ y = 3$

Explanation:

Step1: Identify common factors

The numerator is $x+3$, and the denominator has a factor of $x+3$. These are common factors.

Step2: Find x-value of hole

Set the common factor equal to 0:
$x+3=0$
Solve for $x$: $x=-3$
This is the x-coordinate where the hole occurs, since the common factor makes the function undefined here but can be canceled out (indicating a hole, not a vertical asymptote).

Answer:

A. $x = -3$