### 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.
One thing that would make the expression undefined is if I have a zero in the denominator, because I can't divide by zero.
So I need to avoid values of x that make $\sqrt{5-x}=0$.
To find those values, I can square both sides of the equation and get $5-x=0$.
Solving for x, I get $x=5$.
So x cannot be 5, because that would make the denominator zero.
Another thing that would make the expression invalid is if I have a negative number inside a square root, because I can't take the square root of a negative number.
So I need to avoid values of x that make $x-2<0$ or $5-x<0$.
To find those values, I can solve the inequalities and get $x<2$ or $x>5$.
So x cannot be less than 2 or greater than 5, because that would make one of the square roots negative.
Combining these restrictions, I can say that the domain of the expression is the set of all x such that $2\leq x<5$.
This means that x can be any number between 2 and 5, including 2 but not 5.