Find the Domain y=(x^2-25)/(x-4)

$y = \frac{x^{2} - 25}{x - 4}$

Set the denominator in $\frac{x^{2} - 25}{x - 4}$ equal to $0$ to find where the expression is undefined.

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, 4) \cup (4, \infty)$

Set-Builder Notation:

${x | x \neq 4}$