To solve this equation, we can start by simplifying the expression inside the square root symbol by taking the common denominator.
√x/(x-2) - √(x-2)/(x-2) - 1 = 0
We can simplify this further by combining the two terms inside the square root, which have a common denominator.
[√x - √(x-2)]/(x-2) - 1 = 0
Now we can take the common denominator of the two terms inside the parenthesis and simplify.
[√x - √(x-2) - (x-2)]/(x-2) = 0
Simplifying the numerator further,
[√x - √(x-2) - x + 2]/(x-2) = 0
[√x - x + 2 - √(x-2)]/(x-2) = 0
[√x - x + 2] = √(x-2)
Squaring both sides of the equation,
(√x - x + 2)² = x - 2
Expanding and simplifying,
x² - 2x(√x + 1) + 3 = 0
We can now use the quadratic formula to solve for x:
x = [2(√x + 1) ± √(4x - 8)]/2
x = (√x + 1) ± √(x - 2)
However, we need to make sure that the solution we get satisfies the original equation. We can check by substituting the value of x back into the original equation.
After testing each option, we find that the only solution that satisfies the original equation is x = 9/4.