Rationalize the denominator in the following and simplify completely. Assume all variables under the radicals are nonnegative. \( \frac{\sqrt{x}}{\sqrt{x}-2}=\square \)

To rationalize the denominator of \( \frac{\sqrt{x}}{\sqrt{x}-2} \), multiply both the numerator and the denominator by the conjugate of the denominator, which is \( \sqrt{x} + 2 \): \[ \frac{\sqrt{x}(\sqrt{x} + 2)}{(\sqrt{x}-2)(\sqrt{x}+2)} = \frac{\sqrt{x}(\sqrt{x}+2)}{x - 4} \] Now simplify the numerator: \[ \sqrt{x}(\sqrt{x}+2) = x + 2\sqrt{x} \] Putting it all together gives us: \[ \frac{x + 2\sqrt{x}}{x - 4} \] And there you have it, completely simplified with a rationalized denominator!