Final answer:
The expression (√2x) / (√x - 1) is valid for x > 1, to ensure both the radicand and denominator are well-defined and non-negative.
Step-by-step explanation:
The student's question involves determining for which values of x the expression (√2x) / (√x - 1) makes sense. The expression is valid for real numbers as long as the conditions that the denominator and radicand must be non-negative are met. The denominator (√x - 1) suggests that x must be greater than 1, which ensures that the square root is defined and that the denominator is not zero, which would make the expression undefined. Moreover, the numerator (√2x) implies that x must be non-negative to ensure the radicand is non-negative, and thus, x should be greater than or equal to 0.
However, since the expression must satisfy both conditions simultaneously, the values of x that make the expression valid should be greater than 1. To summarize, the expression makes sense for x > 1.