(5) \( \frac{\sqrt{x}+\sqrt{y}}{x^{1 / 2} x y^{1 / 2}} \)

Did you know you can simplify that expression by factoring out common terms? The numerator, \( \sqrt{x} + \sqrt{y} \), can be tricky, but recognizing it as \( \frac{\sqrt{x} + \sqrt{y}}{\sqrt{xy}} \) allows us to rewrite the entire fraction. Just remember: when working with square roots, it helps to keep your expressions in a manageable format by grouping under the same cube root when possible! Also, if you confront similar expressions, a common mistake is forgetting to combine terms correctly or misplacing the square root's properties! Watch out for signs too; squaring your roots can lead to losing track of negative roots. Simplifying often makes the calculations significantly easier, so take those baby steps in your algebraic dance!