Simiplify. \( \frac{\frac{1}{d}+\frac{1}{e}}{\frac{d^{2}-e^{2}}{d e}} \) The simplified expression is

To simplify the expression   ( (1/d + 1/e) / ((d² – e²)/(de)) ), we start with the numerator:   1/d + 1/e = (e + d) / (de). The denominator is:   (d² – e²)/(de). So, the entire expression becomes:   [(d + e) / (de)] ÷ [(d² – e²)/(de)]. Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus:   [(d + e) / (de)] × [de/(d² – e²)]. Notice that the factors de cancel out:   = (d + e) / (d² – e²). Recognize that d² – e² is a difference of squares and factors as:   d² – e² = (d – e)(d + e). Now the expression becomes:   = (d + e) / [(d – e)(d + e)]. The (d + e) factors cancel (assuming d + e ≠ 0), leaving:   = 1/(d – e). Thus, the simplified expression is 1/(d – e).