To simplify the expression (sqrt(x - 2))/(sqrt(x - 3)), we can first apply the rule that the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator. This gives us the simplified expression:
(sqrt(x - 2))/(sqrt(x - 3)) = sqrt((x - 2) / (x - 3))
Next, we can apply the rule that the square root of a product is equal to the product of the square roots of each factor. This gives us:
sqrt((x - 2) / (x - 3)) = sqrt(x - 2) * sqrt(1 / (x - 3))
Finally, we can apply the rule that the square root of a reciprocal is equal to the reciprocal of the square root. This gives us the simplified expression:
sqrt((x - 2) / (x - 3)) = (sqrt(x - 2) * sqrt(1 / (x - 3))) = (1 / sqrt(x - 3)) / sqrt(x - 2)
Therefore, the simplified expression for (sqrt(x - 2))/(sqrt(x - 3)) is (1 / sqrt(x - 3)) / sqrt(x - 2).