The ratio of sum of two numbers to their difference is 5: 1. What is the ratio of the sum of their squares to the difference of their squares?

Explanation

Given \frac{x+y}{x-y} = \frac{5}{1}. By componendo and dividendo, \frac{x}{y} = \frac{5+1}{5-1} = \frac{6}{4} = \frac{3}{2}. We need \frac{x^2+y^2}{x^2-y^2} = \frac{3^2+2^2}{3^2-2^2} = \frac{9+4}{9-4} = \frac{13}{5}.

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