To solve the inequality (√x - 1)/(√x + 1) > 0, we can follow these steps:

1. Find the critical points by setting the numerator and denominator equal to zero:
√x - 1 = 0 and √x + 1 = 0

Solving these equations, we get:
√x = 1 and √x = -1

Since the square root of a number cannot be negative, we discard √x = -1 as a valid solution.

Therefore, the only critical point is √x = 1, which means x = 1.

2. Create a number line and mark the critical point x = 1 on it.

Number line: (-∞, 1) | (1, +∞)

3. Test a value in each interval to determine the sign of the expression (√x - 1)/(√x + 1).

For x < 1, let's choose x = 0:
(√0 - 1)/(√0 + 1) = (-1)/(1) = -1
Since the expression is negative in this interval, we mark it with a negative sign.

For x > 1, let's choose x = 2:
(√2 - 1)/(√2 + 1) = (1 - 1)/(1 + 1) = 0/2 = 0
Since the expression is zero in this interval, we mark it with a zero.

4. Based on the signs on the number line, we can conclude that the inequality (√x - 1)/(√x + 1) > 0 is satisfied for x < 1.

Therefore, the solution to the inequality is x < 1.