### 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 determine what values of x make the expression valid and meaningful.
One restriction that I have to consider is that I cannot take the square root of a negative number, so I need to make sure that both x-2 and 5-x are non-negative.
This means that I need to solve the inequalities x-2 >= 0 and 5-x >= 0 simultaneously.
Solving for x, I get x >= 2 and x <= 5, which can be combined as 2 <= x <= 5.
This is the interval of x values that satisfy the first restriction.
Another restriction that I have to consider is that I cannot divide by zero, so I need to make sure that the denominator of the expression is not zero.
This means that I need to exclude the value of x that makes 5-x equal to zero, which is x = 5.
So, the domain of the expression is the interval 2 <= x < 5, excluding the endpoint 5.