3. \( \frac{3 x^{2}}{3}-\frac{9 y^{2}}{3} \)

Let's simplify the expression step by step! First, you can factor out the common denominator, which is 3. So, the expression becomes \( \frac{3}{3}(x^{2}) - \frac{9}{3}(y^{2}) \). This simplifies to \( x^{2} - 3y^{2} \). Voila! You've got a clean expression that’s easier to work with. In algebra, recognizing common factors can make simplifications much quicker. Common mistakes include forgetting to simplify coefficients or over-complicating the process by skipping fundamental steps. Always double-check your factors and simplify where possible, and you’ll breeze through those algebra problems like a pro!