To find a common denominator for the fractions in the expression, it's essential to factor the denominators: \( r^2 - 2r = r(r - 2) \) and \( r^2 - 4 = (r - 2)(r + 2) \). The common denominator can be determined by taking the product of the unique factors, which includes \( r \), \( (r - 2) \), and \( (r + 2) \). The discussion emphasizes the importance of clearly stating the problem and using typed equations for clarity. Understanding how to combine fractions using a common denominator is crucial for solving the expression correctly.