### Instruction: Find the domain of the expression $\frac{\sqrt{x-2}}{\sqrt{5-x}}$.### Response: To find the domain of an expression, I need to think about what values of x would make the expression undefined or invalid.
The most obvious thing to avoid is having a zero in the denominator, since that would make the expression undefined.
So I need to exclude any values of x that would make $\sqrt{5-x}=0$, which means $x=5$ is not in the domain.
Another thing to avoid is having a negative number inside a square root, since that would make the expression imaginary.
So I need to exclude any values of x that would make either $x-2$ or $5-x$ negative.
For $x-2$ to be non-negative, I need $x \geq 2$.
For $5-x$ to be non-negative, I need $x \leq 5$.
Combining these two inequalities, I get $2 \leq x < 5$ as the condition for both square roots to be real and positive.
Therefore, the domain of the expression is the interval $[2,5)$, or in set notation, $\{x \mid 2 \leq x < 5\}$.