Rationalize the denominator. Assume that all variables represent positive real numbers. \( \frac{-4}{\sqrt{x}-5} \) \( \frac{-4}{\sqrt{x}-5}=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.)

To rationalize the denominator of \( \frac{-4}{\sqrt{x}-5} \), you multiply the numerator and the denominator by the conjugate of the denominator, which is \( \sqrt{x}+5 \): \[ \frac{-4}{\sqrt{x}-5} \cdot \frac{\sqrt{x}+5}{\sqrt{x}+5} = \frac{-4(\sqrt{x}+5)}{(\sqrt{x}-5)(\sqrt{x}+5)} \] The denominator simplifies as follows: \[ (\sqrt{x}-5)(\sqrt{x}+5) = (\sqrt{x})^2 - 5^2 = x - 25 \] Now, substituting back into the expression we have: \[ \frac{-4(\sqrt{x}+5)}{x-25} \] Distributing the numerator gives: \[ \frac{-4\sqrt{x} - 20}{x-25} \] Thus, the rationalized form of \( \frac{-4}{\sqrt{x}-5} \) is: \[ \frac{-4\sqrt{x} - 20}{x-25} \]