1. The problem is to calculate the expression $$\frac{3x^2 - 4y^2}{3x^2 + 4y^2}$$ for given values of $x$ and $y$ or to simplify it if no values are given. 2. The formula is a rational expression where the numerator is $3x^2 - 4y^2$ and the denominator is $3x^2 + 4y^2$. 3. Important rule: You cannot simplify this expression by canceling terms unless the numerator and denominator share common factors. 4. Since $3x^2$ and $4y^2$ are unlike terms, and the numerator and denominator differ by the sign between the terms, this expression cannot be simplified further algebraically. 5. If you want to evaluate it for specific values of $x$ and $y$, substitute those values into the expression and calculate the result. 6. Without specific values, the expression remains $$\frac{3x^2 - 4y^2}{3x^2 + 4y^2}$$ as the final answer.