If \frac{x}{a}+\frac{y}{b}=a+b and \frac{x}{a^{2}}+\frac{y}{b^{2}}=2, then what is \frac{x}{a^{2}}-\frac{y}{b^{2}} equal to?

Explanation

By observation, substituting x = a^2 and y = b^2 satisfies both equations: \frac{a^2}{a} + \frac{b^2}{b} = a+b and \frac{a^2}{a^2} + \frac{b^2}{b^2} = 1+1=2. Then, \frac{x}{a^2} - \frac{y}{b^2} = 1 - 1 = 0.

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