Find the Domain y=( square root of x-5)/(x-7)

$y = \frac{\sqrt{x - 5}}{x - 7}$

Set the radicand in $\sqrt{x - 5}$ greater than or equal to $0$ to find where the expression is defined.

$x - 5 \geq 0$

Add $5$ to both sides of the inequality.

$x \geq 5$

Set the denominator in $\frac{\sqrt{x - 5}}{x - 7}$ equal to $0$ to find where the expression is undefined.

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

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

Interval Notation:

$[5, 7) \cup (7, \infty)$

Set-Builder Notation:

${x | x \geq 5, x \neq 7}$