In general, we need to start with transforming a complex fraction into a simpler one.

(x^{–1} – y^{–1}) / ( x^{–2} – y^{–2}) = multiply both the numerator and the denominator by x^{2}y^{2}

x^{2}y^{2}(x^{–1} – y^{–1}) / x^{2}y^{2}( x^{–2} – y^{–2}) = simplify by using distributive law (open the parentheses)

(xy^{2 }– x^{2}y) / ( y^{2} – x^{2}) = factor both parts of the resulting fraction

xy(y – x) / ( y – x)( y + x) = cancel the common factors

xy / (x + y)

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