Answer
The domain of this function is all real numbers except $-5$ and $3$.
Work Step by Step
To find the domain of this function, we need to find which values are excluded for $x$. In a rational function, the denominator cannot equal $0$ because the function would be undefined. Therefore, we need to set the denominator equal to $0$ and solve for $x$:
$(x + 5)(x - 3) = 0$
According to the zero product property, if the product of two factors equals $0$, then either factor can be $0$; therefore, we can set each of these factors equal to $0$ and solve:
$x + 5 = 0$ or $x - 3 = 0$
Add or subtract to solve:
$x = -5$ or $x = 3$
These are the numbers $x$ cannot be. Therefore, the domain of this function is all real numbers except $-5$ and $3$.
