To simplify complex problems, start by clearing complex fractions, as demonstrated with the example of \(\frac{\frac{1}{x} - \frac{1}{y}}{\frac{1}{x} + \frac{1}{y}}\). Multiply by a common factor to simplify the expression further, transforming it into \(\frac{y - x}{y + x}\). Then, apply a strategic multiplication to achieve a denominator of the form \(y^2 - x^2\), which allows for cancellation in subsequent steps. This methodical approach helps break down complex problems into manageable parts. The discussion emphasizes the importance of systematic simplification techniques.